PHOTOMETRICAL  MEASUKEMENTS 


PHOTOMETRICAL  MEASUREMENTS 


AND  MANUAL  FOE 


General  practice  of 


WITH   ESPECIAL  EEFEEENCE  TO 
THE  PHOTOMETEY  OF 

ARC  AND  INCANDESCENT  LAMPS 


BY 

WILBUR  M.  STINE,  PH.D. 

WILLIAMSON   PROFESSOR  OF  ENGINEERING  IN  SWARTHMORE  COLLEGE 


OF  THE 

UNIVERSITY 


THE   MACMILLAN   COMPANY 

LONDON;  MACMILLAN  &  CO.,  LTD. 

1909 

All  rights  reserved 


COPYRIGHT,  1900, 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  June,  1900.     Reprinted 
October,  1904 ;  March,  1909. 


J.  S.  Cashing  &  Co.  — Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

THE  rapid  extension  of  the  practice  of  photometrical  meas- 
urements in  this  country,  and  the  general  interest  in  standards 
of  illuminating  power  and  allied  subjects  evidenced  by  fre- 
quent contributions  to  the  current  technical  periodicals,  and 
by  papers  before  the  various  technical  and  physical  associations 
and  societies,  have  been  the  occasion  for  the  preparation  of  this 
work. 

The  topical  form  of  discussion  has  been  followed,  and  a 
certain  amount  of  repetition  has  been  considered  advisable  in 
order  to  permit  concise  treatment  and  definition  of  the  subject 
matter.  In  this  way,  it  was  thought  that  the  book  would 
prove  more  useful  for  reference ;  and  this  has  been  further 
facilitated  by  the  use  of  cross-references. 

That  the  work  might  meet  the  requirements  of  a  larger 
number  of  readers,  many  topics  have  been  somewhat  elabo- 
rately and  simply  discussed  which  might  well  have  been 
abbreviated  for  those  conversant  with  the  principles  of  pho- 
tometry. And  further,  in  the  interest  of  scientific  thorough- 
ness, certain  topics  have  been  mathematically  treated  where 
this  method  would  lead  to  definite  results  capable  of  ready 
application ;  and  at  the  same  time,  where  advisable,  collateral 
paragraphs  are  given  which  describe  the  application  of  these 
discussions  in  order  to  render  the  book  serviceable  as  a  manual. 
On  the  other  hand,  there  are  subjects  whose  mathematical  dis- 
cussion would  lend  no  increased  precision  to  applied  pho- 
tometry, and  these  have  been  either  briefly  indicated  or  wholly 
omitted ;  but  where  possible,  ample  references  have  been  stated 
to  enable  them  to  be  satisfactorily  investigated. 

v 

207833 


VI  PREFACE 

Frequent  references  will  be  found  accompanying  the  text. 
These  occur  in  the  discussion  of  the  historical  development  of 
the  various  phases  of  photometry,  and  considerable  pains  have 
been  taken  to  make  these  as  complete  as  possible ;  also  the 
statement,  both  of  fact  and  conclusion,  has  so  far  as  practicable 
been  accompanied  by  references  to  sources  in  which  the  topics 
are  developed  at  length,  preference  being  given  to  those  which 
discuss  the  subjects  in  an  authoritative  and  thorough  manner. 
The  use  of  copious  references  has  been  dictated  by  a  belief 
that  the  practical  end  is  best  achieved  by  a  thorough  mastery 
of  all  the  details  involved,  and  that  the  authoritative  state- 
ment is  of  slight  value  which  is  not  based  on  a  complete 
knowledge  of  all  the  phases  of  the  subject  at  issue. 

The  common  practice  of  writing  manuals  and  texts  without 
adequate  references  to  the  general  literature  of  their  subject- 
matter  is  reprehensible ;  while,  on  the  other  hand,  the  impar- 
tial method  of  the  exact  scientific  treatise  is  one  that  should 
commend  itself  to  writers  of  all  but  the  most  elementary  texts. 
Otherwise,  the  reader  must  accept  the  written  statement  of  the 
author  without  recourse,  resulting  in  an  attitude  of  depend- 
ence and  uncertainty.  To  the  general  reader,  an  author  may 
be  at  times  obscure  because  of  the  dissimilarity  in  the  attitude 
with  which  the  subject  is  approached.  This  entails  needless 
confusion  and  loss  of  time ;  for,  where  the  author  has  abbre- 
viated, the  reader's  general  knowledge  may  be  inadequate  to 
follow  the  text.  There  are  other  readers  whose  needs  have 
been  considered,  who  have  neither  time  nor  opportunity  to 
follow  references ;  and  these  properly  desire  precise  and  simple 
statements  which  may  be  readily  applied  by  them. 

To  those  who  desire  to  follow  the  practice  of  photometry, 
and  lack  an  adequate  knowledge  of  general  physics,  this  work 
may  appear  too  scientific  for  a  manual,  and  be  too  insistent  on 
details  which  apparently  have  little  significance.  To  such  the 
writer  would  state  that  photometry  is  not  a  simple  and  well- 
defined  subject.  Bare  directions  will  not  suffice,  but  the 


PREFACE  vii 

practician  mast  bring  to  the  task  a  judgment  trained  for 
instrumental  manipulation  and  an  appreciation  of  the  many 
modifying  influences  that  the  results  which  he  obtains  may 
possess  any  value. 

The  work  has  been  written  from  the  literature  of  photometry 
and  with  little  reference  to  existing  works  on  this  subject. 
The  references  accompanying  the  text  will  be  found  to  give  a 
selected  bibliography  of  photometry,  and  should  prove  useful 
both  to  the  investigator  and  the  reader  who  desires  to  pursue 
his  study  independently.  An  admirable  bibliography  of  pho- 
tometry prior  to  1884  is  given  at  length  in  Die  elektro-technische 
Photometric  by  Dr.  Hugo  Krtiss,  in  Hartleben's  Elektro-tech- 
nische Bibliothek. 

The  book  was  originally  planned  to  be  written  with  the  col- 
laboration of  Mr.  Elmer  G.  Willyoung,  who  was  subsequently 
prevented  from  participation  in  its  preparation  by  other  duties. 
The  author  is  indebted  to  him  for  the  suggestion  of  the  work 
and  assistance  in  planning  it. 

It  is  with  pleasure  that  acknowledgments  are  made  to  my 
former  assistant,  Mr.  Truman  P.  Gay  lord,  for  tests  and  data 
bearing  on  the  life  characteristics  of  the  incandescent  lamp; 
to  both  the  Columbia  Incandescent  Lamp  Company  and  the 
General  Electric  Company  for  data  and  the  particulars  of 
processes  of  the  manufacture  of  lamps;  and  to  Queen  and 
Company  for  illustrations.  The  author  also  wishes  to  express 
his  appreciation  of  the  unusual  facilities  of  the  Library  of 
the  Franklin  Institute,  where  the  preparation  for  the  text 
was  accomplished,  and  to  acknowledge  the  numerous  courte- 
sies extended  to  him  by  the  secretary  and  librarian  of  the 
Institute. 


W.  M.  S. 


SWARTHMORE,   PA., 

May  1, 1900. 


CONTENTS 


CHAPTER  I 

THE  GENERAL  PHYSICAL  AND  PHYSIOLOGICAL  PRINCIPLES  OF 
PHOTOMETRY 

PAGE 

Introductory — Physical  Principles  —  Physiological  Optics          .        1 


CHAPTER  II 
PHOTOMETRICAL  QUANTITIES 

Definition  of  Fundamental  Relations  —  The  Practical  Unit  of 
Illuminating  Power  —  Mean  Spherical  Intensity  —  The 
Practice  of  the  Mean  Spherical  Intensity  ....  28 

CHAPTER  in 

PHOTOMETERS 

The  Elements  of  the  Photometer  —  The  Bouguer  Photometer  — 
The  Ritchie  Photometer— The  Rumford  or  Shadow  Pho- 
tometer—  The  Foucault  Photometer  —  The  Wedge-shaped 
Screen  —  The  Paraffine  Diffusion  Screen  —  The  Bunsen 
Photometer  —  The  Lummer-Brodhun  Photometer  —  The 
Leonhard  Weber  Photometer  —  Wedge-shaped  Diffusion 
Plates  — The  Flicker  Photometer  — The  Illumination  Pho- 
tometers —  Various  Photometers  and  Photometrical  Devices 
—  The  Photometer  Bench  —  Spectrophotometry  ...  45 


X  CONTENTS 

CHAPTER  IV 
STANDARDS  OF  ILLUMINATING  POWER 

PAGE 

Introductory — The  English  Candle  —  The  German  Candle  — 
The  Carcel  Lamp  —  The  Methven  Screen  —  The  Pentane 
Standard  —  The  Pentane  Lamp  —  The  Amyl  Acetate  Lamp 
—  The  Arc  Standard  of  Light  —  Incandescent  Platinum 
Standards  — The  Working  Value  of  Light  Standards  .  .  109 

CHAPTER  V 

COMPARISON  LIGHTS,  OR  SECONDARY  STANDARDS  OF 
ILLUMINATING  POWER 

The  Physics  of  the  Incandescent  Lamp  —  The  Incandescent 
Carbon  Filament  as  a  Primary  Standard  of  Light  —  The 
Incandescent  Lamp  as  a  Comparison  Light  —  Oil  and  Gas 
Lamps 171 

CHAPTER   VI 
THE  PHOTOMETRY  OF  THE  INCANDESCENT  LAMP 

Introductory —  The   Photometer  Room  and    its   Apparatus 

The  Practice  of  the  Photometry  of  the  Incandescent  Lamp    196 

CHAPTER  VH 
THE  ARC  LAMP  AND  ITS  PHOTOMETRY 

Introductory  —  The  Physics  of  the  Electrical  Arc  —  The  Practice 

of  Arc  Light  Photometry 220 


CONTENTS  XI 
APPENDIX 

PAGE 

A.  THE  ABSORPTION  OF  LIGHT  BY  GLOBES  AND  THE  ACTION 

OF  REFLECTORS 245 

B.  RECENT  INVESTIGATION   OF   LAMBERT'S   LAW  FOR   THE 

REFLECTION  OF  LIGHT 253 

C.  TABLE  OF  RATIOS  FOR  A  100-PART  PHOTOMETER  BAR    .  258 
INDEX 263 


PHOTOMETRICAL   MEASUREMENTS 


CHAPTER   I 

THE    GENERAL    PHYSICAL     AND     PHYSIOLOGICAL 
PRINCIPLES     OF     PHOTOMETRY 

1.  Photometry  is  a  branch  of  scientific  measurements  which 
deals  with  the  comparison  of  the  illuminating  properties  of 
light  sources. 

All  knowledge  of  illumination  being  ultimately  obtained 
through  the  eye  as  an  organ  of  sensation,  the  subject  of  pho- 
tometry has  a  distinctly  physiological  as  well  as  physical  basis, 
and  each  must  be  carefully  examined  before  the  intricacies  and 
limitations  of  such  measurements  can  be  investigated. 

According  to  the  physical  basis  of  photometry,  light  in 
common  with  heat  is  a  periodic  displacement  in  the  ether  with 
resulting  waves  of  exceedingly  short  periods,  which  vibrate 
transversely  to  their  lines  of  propagation. 

2.  On  measurement.  —  Enlarging  upon  the  similarity  between 
the  physical  properties  of  light  and  heat,  an  illustration  may 
be  taken  from  the  measurement  of  temperature  which  may 
serve  as  an  introduction  to  the  requirements  of  an  instrument 
which  shall  be  suitable  for  the  exact  measurement  of  the  illu- 
minating properties  of  light  sources. 

If  a  mercurial  thermometer  is  placed  at  any  point  in  a  room, 
it  will  presently  register  the  intensity  of  the  heat  in  its  local- 
ity ;  and  when  moved  to  successive  positions  about  the  room 

B  1 


Z  PHOTOMETRICAL   MEASUREMENTS 

it  will  afford  easy  and  certain  measurement  of  the  relative 
intensities  of  the  heat  in  its  several  locations.  As  thus  used 
it  is  a  convenient  instrument  for  determining  the  distribution 
of  temperature  about  the  room. 

Carrying  the  illustration  further,  should  the  room  be  heated 
artificially,  the  thermometer  placed  near  the  source  of  heat 
will  presently  measure  its  intensity. 

Precisely  stated,  the  thermometer  is  an  instrument  designed 
to  measure  the  intensity  of  heat,  and  the  thing  measured  pro- 
duces a  definite  physical  change  in  the  instrument,  a  change 
of  the  volume  of  the  mercury  contained  in  it.  This  change  of 
volume  is  referred  to  a  well-known  unit,  a  degree  of  tempera- 
ture, which  can  be  universally  applied  and  reproduced  under 
the  standard  conditions  of  the  normal  freezing  and  boiling 
points  of  water.  The  sensitiveness,  too,  of  the  thermometer 
may  be  made  very  high. 

3.  The  ideal  photometer.  —  This  discussion  affords  a  criterion 
for  what  is  desirable  in  a  photometer  which  shall  measure  the 
intensity  of  illumination  as  accurately  as  the  thermometer  does 
the  intensity  of  heat.  Following  out  this  illustration,  suppose 
a  simple  and  accurate  photometer  is  placed  successively  at 
different  points  in  a  room  lighted  by  an  incandescent  lamp, 
and  finally  is  directed  toward  the  source  of  light  itself.  The 
readings  thus  obtained  would  afford  not  only  a  precise  knowl- 
edge of  the  intensity  both  of  the  illumination  at  points  in  the 
room  and  of  the  source  of  light,  but  also  of  the  distribution  of 
the  illumination. 

Applying  the  criterion  to  the  photometer,  it  is  found  that 
such  precise  measurements  become  possible  only  when  the 
luminous  property  of  the  light  produces  on  the  photometer 
some  physical  change  whose  character  is  well  known  and 
capable  of  exact  measurement. 

*4.   The  eye  as  a  photometer.  —  A  second  illustration  may  be 
helpful  to  a  clear  conception  of  the  capacity  in  which  the 


PRINCIPLES   OF   PHOTOMETRY  3 

unaided  eye  may  act  as  an  instrument  for  measuring,  or  rather 
estimating,  the  intensity  of  light. 

The  attraction  between  the  moving  magnetic  system  and 
the  fixed  one  of  a  coil  carrying  a  current  and  deflecting  a 
magnet  suspended  within  it,  may  be  numerically  expressed  by 
the  general  law  of  attraction, 

F=k^.  (1) 

What  is  here  emphasized  is  that  the  constant  k  refers  to  the 
ability  of  the  medium  between  the  two  attracting  systems  to 
transmit  a  definite,  mutual-stress  disturbance.  Should  the 
transmitting  power  of  the  medium  change  from  day  to  day,  or, 
indeed,  from  hour  to  hour,  and  be  susceptible  to  fatigue,  gal- 
vanometry  would  become  impossible  ;  for  the  measurements 
of  electric  currents  made  at  different  times  would  not  be 
comparable. 

In  like  manner  a  general  visual  law  may  be  stated,  which 
shall  define  the  degree  of  the  sensation  of  a  luminous  source 
as  a  function  of  its  physical  intensity.  This  law  may  be 
phrased 


the  symbols  referring,  S,  to  the  sensation;  P,  to  the  inten- 
sity of  the  source  of  light  ;  and  d,  to  the  distance  between  the 
eye  and  the  source.  The  significant  symbol  is  the  constant  a, 
which  connects  the  sensation  with  a  purely  physical  relation 

P 

d* 

In  reality,  what  has  been  attempted  in  this  expression  is  an 
equation  between  a  psychological  and  a  physical  quantity,  the 
correlation  of  these  two  classes  of  phenomena  being  affected 
through  the  constant  a. 

The  eye  and  its  associated  neural  structures  act  as  the 
medium  in  this  correlation.  Regarding  the  optical  structures 


4  PHOTOMETRICAL   MEASUREMENTS 

as  a  mere  apparatus  they  are  seen  to  lack  constancy  of  action 
and  to  be  subject  to  the  unknown  quantitative  action  of 
fatigue.  The  quantity  a  varies  in  an  irregular  manner  from 
time  to  time,  and  one  can  not  depend  upon  it  to  show  succes- 
sively constant  values.  Fatigue,  nutrition,  and  the  general  con- 
dition of  the  nervous  system,  all  have  their  influence  upon  it. 

To  pursue  the  subject  further,  —  for  this  is  one  of  the  per- 
plexing psycho-physical  problems  that  enter  into  photometry, 
—  no  dependence  can  be  placed  upon  the  memory  of  an  amount 
of  a  sensation.  Should  the  quantity  we  have  called  a  be  con- 
stant on  two  successive  trials,  separated  by  a  short  time-inter- 
val, as  an  hour,  no  one  can  state  with  the  perfect  definiteness 
of  the  readings  of  a  galvanometer,  that  the  two  light  sources 
viewed  in  succession  were  of  equal  intensity. 

Thus  no  one  can  depend  upon  the  eye  to  compare  the 
intensity  of  one  light  source  with  that  of  another.  In  these 
cases  the  eye  is  seen  to  lack  the  essential  requirements  for  an 
apparatus  for  the  measurement  of  the  intensity  of  light. 

A  much  greater  complication  is  introduced  when  the  change 
of  the  sensation  with  respect  to  the  variation  of  the  exciting 
light  source  is  considered.  This  phase  will  be  subsequently 
discussed  (page  15). 

PHYSICAL  PRINCIPLES 

5.  On  ether  waves.  —  Light  may  be  denned  for  our  purpose, 
as  transversely  vibrating  ether  waves,  whose  frequency  of 
vibration  is  such  that,  falling  upon  the  retina  of  the  eye,  they 
produce  the  sensation  of  sight.  This  definition  of  light  is 
usually  termed  a  subjective,  or  physiological  one,  but  it  is 
adopted  as  the  most  suitable  one  for  the  discussion  of  the 
principles  of  photometry. 

A  wave  train  is  transmitted  through  the  ether  by  series  of 
successive  displacements,  which  are  repeated  in  all  respects  in 
equal  but  very  short  periods  of  time.  This  may  be  illustrated 
by  a  diagram  (Fig.  1).  An  undisturbed  chain  of  particles,  A, 


PRINCIPLES   OF   PHOTOMETRY  5 

B  •••  0)  is  shown,  whose  members  are  so  elastically  connected 
with  each  other  that  one  in  moving  pulls  upon  its  fellow. 
When  the  particle  A  is  set  into  transverse  vibration,  it  com- 
municates a  similar  movement  in  succession  to  B,  C,  D  ••• 
and  0,  and  the  chain  vibrates  like  a  stretched  string. 

After  the  disturbance  has  reached  the  particle  0,  the  position 
of  each  member  of  the  chain  is  shown  by  the  points  a,  6,  c,  d 
•  ••  o.  This  latter  arrangement  of  the  particles  illustrates  a 
complete  wave  form,  and  a  succession  of  similar  wave  forms 
constitutes  a  wave  train.  The  line  XY  is  the  axis  of  the  wave, 
and  the  distance  from  a  to  o,  denoted  by  Z,  is  the  wave  length. 
The  greatest  displacement  of  the  particles  from  the  axis  XY 

ABCDEFGHIJKLMNO 


occurs  at  p'  and  r',  and  their  distance,  pp'  or  rr',  from  the  axis 
is  called  the  amplitude  of  the  wave.  The  time  which  is 
required  for  the  motion  of  the  particle  a  to  reach  the  particle 
o  is  the  period  of  the  vibration ;  and  the  number  of  times  this 
disturbance  is  completely  repeated  in  a  second  is  the  frequency. 
Such  wave  trains  are  propagated  through  the  ether  with  a  defi- 
nite velocity,  and  if  this  is  denoted  by  v,  the  period  of  the  wave 
by  T,  and  the  frequency  by  /,  the  length  of  the  wave  being  X, 
the  relations  between  these  various  quantities  are 

r  =  i,  (3) 

and  X  =  OT  =  ^-  (4) 


6  PHOTOMETRICAL  MEASUREMENTS 

The  most  accurate  determination  of  the  velocity  of  the  prop- 
agation of  light  through  a  vacuum  is  not  far  from  299,860,000 
metres  per  second ;  this  particular  value  having  been  obtained 
by  Newcomb  at  Washington  in  1882.* 

6.  Visible    light.  —  The    ether   waves    which    produce   the 
phenomena  of  heat  and  light  are  inherently  the  same,  though, 
in  general,  the  vibrations  which  are  commonly  termed  heat 
waves  have  a  much  lower  frequency  than  the  vibrations  giving 
rise  to  visible  light.     It  is  essential  to  note  that  the  distinction 
between  heat  and  light  is  largely  physiological  and  subjective : 
the  ether  waves  which  excite  the  sensation  of  warmth  on  the 
body  are  known  as  heat  waves ;  while  light  waves  are  those 
having  a  suitable  frequency  to  produce  sight  sensations  when 
received  on  the  retina  of  the  eye.      Thus  the  physiological 
distinction  amongst  ether  waves  is  based  on  the  particular 
kind  of  sensation  excited  by  them ;  and  their  physical  distinc- 
tion is  one  of  amplitude  and  frequency. 

Light,  or  visible  ether  waves,  ranges  in  frequency  between 
392  x  1012  per  second,  corresponding  to  the  extreme  red  of 
the  spectrum,  and  760  x  1012  per  second,  the  extreme  limit  of 
the  violet  end  of  the  spectrum.  These  are  merely  general 
limits,  and  are  not  constant  for  the  same  eye  nor  for  different 
eyes. 

7.  The  physical  meaning  of  colour.  —  In  the  physical  sense 
the  colour  of  light  waves  is  defined  by  their  particular  pitch  or 
frequency ;  and  one  light  wave  differs  from  another  in  colour 
according  as  its  frequency  is  higher  or  lower  than  that  of  the 
wave   with  which   it   is   compared;    and   there  are  as  many 
physical  colours  in  the   range  of  visible   light   as   there  are 
possible  frequencies  between  the  limits  of  392  x  1012  and  760  x 
1012.     Yet  so  closely  are  the  physical  and  physiological  aspects 
of  colour  related,  that  the  physical  colours  are  associated  into 

*  See  Preston,  The  Theory  of  Light,  page  505,  for  a  table  of  the  most 
accurate  determinations  of  this  constant. 


PRINCIPLES    OF    PHOTOMETRY  7 

certain  groups  corresponding  to  the  manner  in  which  the 
spectrum  of  white  light  affects  the  eye.  If  the  entire  extent 
of  these  spectrum  groups  be  represented  by  a  scale  divided  into 
one  hundred  equal  parts,  the  space  occupied  by  each  colour 
group  as  given  by  Rood,*  is :  — 

TABLE  I 
EXTENT  OF  COLOUR  GROUPS  IN  THE  NORMAL  SPECTRUM 

Red  begins  at      .  '     .       •. 00.0 

Pure  red  ends,  orange-red  begins  at   .         .         .  •       .  33.0 

Orange-red  ends,  orange  begins  at      ....  43.4 

Orange  ends,  orange-yellow  begins  at          ...  45.9 

Orange-yellow  ends,  yellow  begins  at          ...  48.5 

Yellow  ends,  greenish  yellow  begins  at       ...  49.8 

Greenish  yellow  ends,  full  green  begins  at          .         .  59.5 

Full  green  ends,  blue-green  begins  at          ...  68.2 

Blue-green  ends,  cyan-blue  begins  at  .         .         .         .  69.8 

Cyan-blue  ends,  blue  begins  at    .         .     '   .         .        .  74.9 

Blue  ends,  violet-blue  begins  at 82.3 

Violet-blue  ends,  pure  violet  begins  at         ...  94.0 

If  the  frequency  of  a  colour  wave  is  known  at  any  point  of 
this  scale,  the  corresponding  frequency  and  wave  lengths  at 
other  points  may  be  calculated  by  the  equations  (3)  and  (4) 
on  page  5.  In  all  cases  the  length  of  a  light  wave  is  a  very 
small  dimension,  and  for  their  comparison,  a  unit  length  of  the 
one-millionth  part  of  a  millimetre  may  be  taken.  The  group- 
ing of  wave  lengths  by  this  unit  is,  according  to  Rood  f :  — 

TABLE  II 
WAVE  LENGTHS  IN  MULTIPLE  OF  10~6  MILLIMETRE 

Centre  of  red 700.0 

Centre  of  orange-red 620.8 

Centre  of  orange         .......         597.2 

*  Modern  Chromatics,  or  Text-book  of  Color,  O.  N.  Rood,  page  24. 
t  Rood,  reference  cited,  page  26. 


PHOTOMETRIC AL   MEASUREMENTS 

Centre  of  orange-yellow 587.9 

Centre  of  yellow 580.8 

Centre  of  full  green 527.1 

Centre  of  blue-green  .......  508.2 

Centre  of  cyan-blue 496.0 

Centre  of  blue 473.2 

Centre  of  violet-blue 438.3 

Centre  of  pure  violet 405.9 

8.  Regular  and  diffused  reflection.  —  Light  rays  falling  on  a 
surface  are  reflected,  with  a  certain  loss  due  to  absorption,  in 
two  distinct  ways.     Falling  on  a  plane  surface,  the  path  of 
both  the  incident  and  reflected  rays  makes  an  equal  angle  with 
the  normal  to  the  reflecting  surface.     This  is  variously  termed 
regular  or  specular  reflection;  and  its  characteristic  is,  that  it 
produces  a  glare  or  an  image  of  the  light  source  in  the  eye, 
while  the  reflecting  surface  is  not  visible  through  such  rays. 
Mirrors    and    glazed    paper,    or   very    white,    smooth    paper, 
placed  at  an  angle  of  45°,  regularly  reflect  the  light  in  various 
amounts. 

If  the  surface  is  rough,  the  light  will  be  diffused  in  all  direc- 
tions; and,  while  no  image  of  the  light  source  is  seen,  the 
reflecting  surface  itself  is  visible.  This  is  termed  either  diffused 
or  irregular  reflection. 

9.  Selective  absorption  by  reflection  and  transmission  of  light. 
—  Any  given  set  of  molecules  may  absorb  the  energy  of  light 
waves  only  when  there  is  correspondence  between  the  molec- 
ular  periods    of   vibration   and   the   frequency   of   the   light 
waves.     Substances  differ  widely  in  their  powers  of  absorption, 
and  to  this  is  due  the  variety  of  colour  of  objects. 

When  light  falls  on  a  surface  which  absorbs  all  but  the 
slower  light  waves  and  reflects  these,  the  surface  will  appear  red. 

Similarly,  when  white  light  passes  through  a  layer  which  is 
transparent  to  green  rays,  and  absorbs  all  other  frequencies, 
the  quality  of  the  incident  light  will  be  changed  to  green,  after 
transmission  through  the  plate. 


PRINCIPLES    OF   PHOTOMETRY 


9 


10.  Selective  diffusion.  —  Closely  associated  with  these  phe- 
nomena is  a  third,  called  selective  diffusion.     Opal  glass  owes 
its  peculiar  properties  to  some  very  finely  divided  white  solid 
suspended  in  a  matrix  of  clear  glass.     The  fineness  of  the  sus- 
pended particles  is  comparable  to  the  length  of   blue   light 
waves,  while  the  particles  are  too  small  sensibly  to  reflect  the 
longer  rays  of  the  spectrum.     This  topic  will  be  further  dis- 
cussed in  connection  with  its  application  to  diffusing  screens 
(page  48). 

11.  Total  reflection  of  light. — When  light  passes  from  one 
medium  into  a  rarer  one,  the  rays  are  refracted  from  a  normal 


^/V~^V7/^/^^^^^ 


FIG.  2. 


to  the  separating  surface.  Thus,  in  Fig.  2,  OA  is  the  path  of 
a  ray  in  a  dense  medium  such  as  glass,  whose  incident  angle  to 
the  surface  PQ  is  i,  and  AA'  is  the  path  in  air  refracted  at  an 
angle  r.  These  angles  of  incidence  and  refraction  bear  a  con- 
stant relation  for  any  given  transparent  substance  in  air,  such 

that 

sin  i  __ 

sin  r 


(5) 


As  the  angle  of  incidence  increases,  it  will  eventually  attain 
a  value  i',  such  that  the  ray  OA"'  will  be  refracted  in  the  plane 


10 


PHOTOMETRICAL  MEASUREMENTS 


PQ.  This  particular  value  for  the  angle  of  incidence  is  known 
as  the  critical  angle  for  that  substance  ;  and  in  crown  glass,  for 
example,  its  value  is  about  40°  30'. 

If  this  critical  value  is  exceeded,  the  ray  of  light  will  not 
emerge  into  the  air,  but  be  totally  reflected  back  through  the 
glass,  as  is  the  case  when  the  ray  OB  makes  an  incident  angle 
/  with  the  normal  to  PQ.  The  ray  then  obeys  the  law  of 
reflected  light. 

One  application  made  of  this  principle  is  shown  in  Fig.  3, 

which  represents  a  sec- 
tion of  a  rectangular 
prism.  A  beam  of 
light  AO  perpendicu- 
larly incident  on  a  face 
of  the  prism,  is  totally 
reflected  at  0,  and 
emerges  along  the  path 
OB  perpendicular  to  the 
second  face  of  the  prism. 
In  such  a  case,  practi- 
cally none  of  the  light  is 
dispersed,  and  its  direc- 
tion is  changed  without 
sensible  loss  in  intensity. 

12.  Reflection  of  light  from  various  surfaces.  — The  proportion 
of  light  reflected  from  a  particular  surface  depends  both  upon 
the  angle  of  incidence  and  the  condition  of  the  surface.  The 
latter  is  by  no  means  constant  in  its  effect  on  light ;  for  as  a 
surface  becomes  rough  and  soiled  by  exposure,  its  reflecting 
power  is  proportionately  decreased.  Data  of  this  character 
are  to  be  taken  as  suggestive  rather  than  final.  An  interest- 
ing set  of  values  is  given  by  W.  E.  Sumpner.*  The  first  four 
values  were  determined  with  great  care,  the  remaining  ones 
are  only  approximate  :  — 


FIG.  3. 


*  Philosophical  Magazine  ;  35,  1893,  page  88. 


PRINCIPLES   OF   PHOTOMETRY  11 

Per  cent 

White  blotting  paper 82.0 

White  cartridge  paper          ......  80.0 

Tracing  cloth,  polished  side 35.0 

Tracing  paper 22.0 

Ordinary  foolscap 70.0 

Ordinary  newspaper 50  to  70.0 

Yellow  wall  paper        .......  40.0 

Blue  paper 25.0 

Dark  brown  paper 13.0 

Deep  chocolate  paper 4.0 

Clean  plane  deal  surface 40  to  50.0 

Yellow  painted  wall,  clean 40.0 

Black  cloth 1.2 

Black  velvet         .        .        .        .  '      .        .        .        .  0.4 

13.   Emissivity,  or  surface  conductivity  for  heat  and  light.  — 

This  property  enables  the  superficial  layer  of  a  body  heated  to 
incandescence,  to  radiate  or  pass  outward  into  space  both  heat 
and  light  radiations.  If  the  surface  was  of  such  a  nature  that 
it  would  not  give  out  dark  heat  rays,  but  pass  light  rays  alone, 
a  condition  for  ideal  illumination  would  be  attained;  a  con- 
dition which  is  unknown,  but  which  is  approached  as  the 
temperature  of  the  incandescence  of  the  body  is  increased. 

The  hot  carbon  surfaces  of  the  arc  and  incandescent  lights 
—  aside  from  the  amount  of  heat  lost  by  conduction  to  the  air 
and  masses  in  contact  —  pass  the  transformed  electrical  energy 
and  radiate  it  into  space.  In  the  arc  light  a  greater  proportion 
of  the  energy  emitted  and  radiated  produces  light  waves  than 
in  the  case  of  the  incandescent  lamp,  since  the  temperature  is 
higher. 

Again,  the  emissivity  of  a  surface  is  to  a  great  extent  a  func- 
tion of  its  character,  whether  it  be  hard  and  bright,  or  rough 
and  dark.  The  emissivity  of  the  dull,  black  carbon  filament 
for  both  light  and  heat  radiations  is  greater  than  that  of  a 
brightly  polished,  flashed  surface.  In  general,  polish  on  a 
surface  lowers  its  emissivity.  The  polish  imparts  greater 
reflecting  power,  and  more  heat  and  light  rays,  if  the  body 


12  PHOTOMETRICAL   MEASUREMENTS 

is   incandescent,  are  reflected  inwardly  instead  of  being  radi- 
ated outwardly,  and  their  energy  is  retained. 

The  surface  emissivity  of  a  body  may  be  denned  as  its  rate 
of  losing  heat  or  light  energy;  and  it  is  measured  by  the 
quantity  of  energy  lost  in  one  second  from  unit  area  of  sur- 
face, with  unit  difference  of  temperature.* 

PHYSIOLOGICAL  OPTICS 

14.  The  physiological  meaning  of  colour.  —  A  clear  under- 
standing of  the  physiological  meaning  of  colour  is  necessary 
to  follow  the  intricacies   and   difficulties  of  photometry  and 
standards  of  illumination.     The  physiological  basis  of  colour 
is  a  particular  mode  of  nerve  stimulation  in  the  retina  of  the 
eye.     This  is  transmitted  to  the  brain  by  the  optic  nerve  tract 
and  thence  there  results  a  colour  sensation.     Each  kind  of 
colour  sensation  is  probably  connected  with  a  definite  nerve 
stimulus.      However,  it  is  erroneous  to  conclude  that  these 
definite  nerve  stimuli  are  necessarily  definitely  excited.     They 
are  ordinarily  excited  by  ether  waves  of  frequencies  already 
described,  yet  colour  sensation  results  when  the  optic  nerve 
tract   is   excited  by  an   electric  current,  and  by  mechanical 
shock,  or  pressure.     Nor  is  a  particular  kind  of  colour  sensa- 
tion excited  only  by  ether  waves  of  frequencies  corresponding 
to  that  colour  in  the  spectrum ;   as  an  instance,  a  red  colour 
sensation  is  induced  in  varying  degrees  by  practically  all  the 
frequencies  of  visible  ether  waves. 

15.  The  Young-Helmholtz  theory  of  colour  vision.  — The  com- 
pound character  of  white  light  is  shown  by  spectrum  analysis, 
and  it  is  reasonable  to  suppose  that  the  colour  sensation  corre- 
sponding to  white  light  is  not  a  simple  sensation,  in  that  it  is 
due  to  one  special  mode  of  nervous  stimulus.     Careful  experi- 
mentation has  established  the  correctness  of  this  supposition. 
By  means  of  the  rotation  of  coloured  sectors,  so  rapidly  that 

*  Consult  Preston,  Theory  of  Heat,  pages  442  and  460. 


PRINCIPLES    OF   PHOTOMETRY 


13 


the  excitation  of  the  first  sector  persisted  until  the  eye  was 
affected  by  the  colour  of  the  last  sector,  thus  superposing  the 
colours  of  all  the  sectors,  Maxwell  showed  that  the  sensation 
of  white  light  could  be  produced  by  a  variety  of  combinations 
of  colours.  Finally  it  has  been  shown  that  the  sensation  of 
white  light  may  be  obtained  by  the  rotation  of  three  sectors, 
representing  three  of  the  principal  colour  bands  of  the  spectrum 
in  certain  proportions, — red,  green,  and  violet.  Extending  the 
same  method  of  investigation,  Maxwell  was  able  to  produce 
practically  the  entire  range  of  colour  sensations,  by  varying 
the  relative  areas  of  the  red,  green,  and  violet  sectors. 


FIG.  4. 

In  1802  Thomas  Young  *  published  a  theory  of  colour  vision, 
which  supposed  the  retina  of  the  eye  to  be  primarily  sensitive 
only  to  red,  yellow,  and  blue  light  stimuli.  Subsequently  he 
adopted  red,  green,  and  violet  as  the  primary  colours,  and  this 
latter  selection  of  colours  is  still  adhered  to  by  the  advocates 
of  this  theory.  Later  on  this  theory  received  such  careful 
experimental  exposition  through  the  investigations  of  Helm- 
holt  z  and  Maxwell,  that  it  is  generally  accepted  as  a  satisfac- 
tory working  hypothesis  for  the  phenomena  of  colour  vision. 
*  Philosophical  Transactions,  Part  I,  1802,  page  21. 


14  PHOTOMETRICAL   MEASUREMENTS 

The  Young-Helmholtz  theory,  as  it  is  now  called,  is  usually 
discussed  by  the  aid  of  a  diagram  due  to  Helmholtz,*  and 
shown  in  Figure  4.  The  curves  R,  G,  and  V,  refer  to  the  rela- 
tive intensities  of  the  primary  colour  sensations  of  red,  green, 
and  violet.  It  is  seen  from  this  diagram  that  the  red  primary 
colour  sensation  is  excited  in  varying  intensities  by  practically 
all  the  frequencies  of  the  visible  spectrum,  as  is  also  the  case 
with  the  green,  and  violet  primary  colour  sensations. 

Any  given  colour  sensation  is  thus  a  compound  one ;  for  ex- 
ample, a  yellow  is  due  to  a  strong  excitation  of  the  green 
primary  colour  sensation  combined  with  a  certain  degree  of 
the  red,  and  less  of  the  violet ;  while  for  a  blue  colour  sensa- 
tion, the  primary  violet  predominates  with  less  of  the  green 
and  red. 

The  criterion  for  normal  white  light  is,  accordingly,  a  light 
which  will  have  such  relative  intensities  throughout  the  length 
of  its  visible  spectrum  that  it  will  excite  the  primary  colour 
sensations  in  the  ratios  indicated  in  the  Helmholtz  diagram,  or 
a  similar  one,  should  this  not  be  found  to  represent  the  normal 
action  of  average  eyes. 

Though  our  knowledge  of  the  anatomy  and  physiology  of 
the  eye  neither  confirms  nor  refutes  this  theory  of  colour 
sensations,  the  conclusions  arrived  at  concerning  white  and 
coloured  lights  are  founded  on  experimental  evidence,  and  they 
can  not  be  seriously  modified  whatever  theory  may  be  adopted. 
This  is  the  sense,  that  of  a  working  hypothesis,  in  which  the 
Young-Helmholtz  theory  of  colour  vision  will  be  referred  to  in 
subsequent  portions  of  this  work. 

16.  Quantitative  judgments  of  light.  —  The  question  natu- 
rally arises  in  such  discussions,  Does  the  intensity  of  a  sen- 
sation bear  any  relation  to  the  magnitude  of  its  stimulus? 
For  illustration,  suppose  two  incandescent  lights  be  looked  at 
in  succession  in  such  a  manner  that  the  eye  receives  no  light 

*  Helmholtz,  Physiolog.  Optik,  page  291 ;  also  consult  Ladd,  Physio* 
logical  Psychology,  page  339  ;  and  Foster,  Physiology,  page  899. 


PRINCIPLES   OF  PHOTOMETRY  15 

not  coming  from  one  source  or  the  other.  These  lights  are  simi- 
lar in  colour,  and  one  is  n  times  as  bright  as  the  other.  Will 
the  sensation  in  one  case  be  n  times  as  intense  as  in  the  other  ? 
Again,  it  must  be  recognized  at  the  very  outset  that  sen- 
sations are  eventually  psychological,  and  though  received 
through  material  agencies,  are  themselves  neither  matter  nor 
energy.  Under  such  conditions  it  is  to  be  anticipated  that 
sensations  are  not  rigidly  subject  to  quantitative  expression, 
as  are  all  relations  of  matter  and  energy. 

17.  Proposed  law  of  the  intensity  of  sensations. — This  sub- 
ject has  been  investigated  by  exhaustive  experiments  by  Fech- 
ner,  Weber,  Helmholtz,  and  others ;  and  though  a  law  rigidly 
adhered  to  has  not  been  discovered,  yet  the  intensity  of  normal 
sensations  has  been  found  to  follow  somewhat  closely  a  relation 
known  as  "  Fechner's  Law." 

18.  Fechner's  law.  —  The  simplest  statement  of  this  law  is 
that  the  differences  in  sensations  vary  as  the  logarithm  of  the  ratio 
of  the  stimuli  producing  the  differing  sensations. 

If  the  strength  of  the  sensation  was  directly  proportional  to 
the  excitation,  a  light  A,  which  is  twice  as  strong  as  a  similar 
light,  B,  would  produce  a  sensation  a  =  2  6,  and  the  mind  could 
in  general  form  fairly  accurate  judgments  of  the  relative  inten- 
sities of  lights.  But  the  actual  relation  between  the  strength 
of  the  sensation  and  its  stimulus  being  so  complex,  the  result- 
ing judgment  is  confused,  and  comparisons  of  the  intensity  of 
illumination  by  the  unaided  eye  are  entirely  unreliable.  This 
is  an  essential  reason  for  confining  the  photometrical  measure- 
ments of  illumination  to  the  comparison  of  equally  lighted 
fields. 

19.  Mathematical  discussion  of  Fechner's  law. — On  the  sup- 
position that  a  definite  relation  exists  between  the  strength  of 
a  sensation  and  its  stimulus,  if  the  strength  of  the  sensation  be 
denoted  by  S,  and  of  the  stimulus  by  /, 

S  =/(/).  (6) 


16  PHOTOMETRICAL  MEASUREMENTS 

It  has  been  experimentally  established  that  the  smallest  dis- 
tinct change  which  the  average  trained  eye  can  distinguish  in 
the  illumination  of  an  object  is  about  one  part  in  one  hundred.* 
This  ratio  seems  to  obtain  over  quite  a  range  of  light  sensa- 
tions, and  if  the  illumination  be  expressed  in  candle-power 
units,  it  would  be: 

Total  Illumination  Least  Observed  Change 

10  candles  .....        0.1  candle 

20       "  .....        0.2      " 

50       "  ......        0.5      « 

100       "  .....        1.0      " 

The  essential  fact  to  note  in  such  a  series  of  values  is  that 
the  least  observable  change  of  the  illumination  is  not  a  constant 
difference  of  candle  power,  but  that  it  forms  a  constant  ratio  to 
the  total  impressed  illumination. 

Assuming  that  the  least  possible  change  A7  in  the  illumina- 
tion J,  which  the  eye  can  detect  is,  within  a  certain  range,  the 
one-hundredth  part  of  the  impressed  illumination,  the  assump- 
tion may  be  given  the  statement, 

y  =  0.01.  (7) 

The  significance  of  this  constant  quantity  is  that  the  illu- 
mination changes  in  each  case  by  a  fixed  part  of  itself. 

Denoting  the  corresponding  change  in  the  sensation  S  by  A$, 


(8) 

A  being  used  as  an  equating  constant  between  the  change  of 
sensation  and  its  correlative  change  of  stimulus.     Then 


*  Ladd,    Physiological    Psychology,  page  366  and  Chapter  V  ;   and 
Helmholtz,  Physiolog.  Optik,  pages  312-316. 


PRINCIPLES  OF  PHOTOMETRY  17 

By  an  extension  of  this  method  it  follows  that  the  stimulus- 
rate-of-change  of  the  sensation  in  the  last  equation  is,  for  all 
values  of  the  changes  in  S  and  7, 

i-f 

Then  for  exceedingly  small  changes  in  S  and  J, 

<fe  =  ^y,  (11) 

and  by  integration,  S  =  A  log  /+  c,  (12) 

which  determines  the  relation  between  the  quantity  of  a  sensa- 
tion and  that  of  its  stimulus  provided  the  constants  are  known. 
The  law  of  the  difference  of  sensations  is  of  greater  interest 
in  this  connection.  This  law  may  be  derived  from  the  last 
equation  by  writing  in  succession, 

S2  =  J.log/2  +  c,  (13) 

and  Si  =  A  log  JL  -f  c ;  (14) 

and  by  subtraction,  S2  —  Si  =  A  log—-  (15) 

I\ 

20.  Complementary    colours.  —  Aside    from    any    theory    of 
colour  vision,  it  is  an  interesting  experimental  fact  that  the 
colour  sensation  of  white  light  may  be  produced  by  various 
combinations   of  only  two  colours.      Such   colour  pairs   are, 
among  others,  red  and  very  greenish  blue ;  yellow  and  ultra- 
marine blue ;  and  greenish  yellow  and  violet.* 

21.  Fatigue   of   the   eye.  —  A    peculiar    psychological    phe- 
nomenon occurs  through  fatigue  of  the  eye  after  looking  at  a 
brightly  illuminated  object.     If  a  red  surface  has  been  looked 
at  intently  for  some  time,  and  the  eye  then  turned  to  a  white 
or  gray  surface,  instead  of  showing  in  its  proper  colour,  it 

*  Helmholtz,  Physiolog.  Optik,  page  277. 


18  PHOTOMETRIC  AL  MEASUREMENTS 

appears  to  be  greenish  blue.  Similarly,  through  fatigue,  an 
orange  surface  will  produce  a  blue  after-colour,  and  yellow  an 
indigo  blue.* 

Such  phenomena  are  not  without  importance  in  photometry, 
and  in  the  comparison  of  lights  of  different  colours  are  a  pos- 
sible source  of  confusion  and  error. 

22.  Exaggerated  contrast.  —  If  alternate  strips  of  white  and 
black  be  looked  at  closely,  the  edges  of  the  white  strips  will 
appear  much  brighter  by  contrast  with  the  black  than  their 
central  portions.     The  judgment  of  the  intensity  of  the  illu- 
mination, formed  under  such  conditions,  would  be  out  of  pro- 
portion to  the  real  stimulation  of  the  eye. 

In  the  preceding  paragraph  it  was  explained  that  comple- 
mentary colours  were  seen  by  successive  contrast — the  eye 
being  moved  from  one  surface  to  another.  But  such  phe- 
nomena of  complementary  colours  may  occur  by  simultaneous 
contrast,  though  in  a  lesser  degree.  If  lights  of  different  col- 
ours are  brought  together  on  a  surface,  the  edge  of  each  will  not 
appear  in  its  true  colour,  but  be  blended  to  some  extent  with 
its  complementary  colour.  This  confusion  disappears  when  the 
two  colours  are  separated  by  a  narrow  band  of  black. 

A  thorough  comprehension  of  the  foregoing  facts  of  fatigue 
and  contrast  is  needed  to  follow  the  theory  of  such  screens  as 
the  Lummer-Brodhun. 

23.  Proper  conditions  for  comparing  lights.  —  The  influence 
of  fatigue  in  producing  complementary  colours  and  exaggerated 
contrast  alone  renders  accurate  estimations  of  relative  bright- 
ness practically  impossible.     By  reducing  photometrical  meas- 
urements to  cases  of  comparison  of  lights  of  similar  colour  and 
equal  intensity  on  the  observing  screen,  such  disturbances  are 
almost  wholly  avoided. 

24.  The  effects   of  the  persistence  of  vision.  —  If   repeated 
stimuli  succeed  each  other  within  their  period  of  persistence. 

*  Foster,  Physiology,  page  934. 


PRINCIPLES   OF    PHOTOMETRY  19 

the  sensation  which  they  will  produce  is  that  of  continuous 
light.  When  the  interval  between  the  stimuli  is  very  nearly 
equal  to  the  time  of  dying  away  of  a  sensation,  the  light  will 
appear  to  "flicker."  This  principle  is  made  use  of  in  the 
"Flicker"  photometer. 

If  the  interval  between  successive  stimuli  is  distinctly 
longer  than  the  period  of  persistence,  the  light  will  appear 
intermittent.  Experimental  data  show  that  when  the  stimu- 
lus interval  is  shortened,  the  intermittent  light  appears 
flickering  and  finally  continuous,  and  that  the  particular 
interval  which  marks  the  passage  from  a  flickering  to  a 
continuous  light  sensation  is,  for  weak  light  and  the  aver- 
age eye,  about  ^  second,  and  for  very  strong  light  J? 
second.*  These  principles  are  also  employed  in  the  rotating 
sector  disk. 

25.  Illumination.  —  This  is  a  subject  over  which  many 
obscurities  and  errors  of  photometry  have  originated,  and 
precision  in  photometrical  measurements  requires  a  clear  com- 
prehension of  the  elements  which  enter  into  the  definition  of 
illumination.  The  term  may  be  provisionally  defined  as  the 
quality  and  quantity  of  light  which  stimulates  the  eye  in 
discrimination  of  outlines  and  perceptions  of  colours;  and 
emphasis  is  laid  upon  both  the  qualitative  and  quantitative 
aspects  of  illumination. 

Here  again  the  primary  fact  is  psychological,  —  the  light 
sensation,  —  and  one  must  proceed  outward  through  the  physio- 
logical excitation  of  the  retina,  to  the  physical  disturbances 
producing  it. 

The  influence  of  the  quantity  of  light  is  defined  by  Fechner's 
law,  yet,  at  the  basis  of  a  satisfactory  definition  of  illumination, 
is  that  certain  amount  of  light  which  is  requisite  for  clearly 
and  easily  seeing  the  outlines  of  objects.  To  this  must  be 
added  the  proper  quality  of  light  to  bring  out  the  colours  of 
objects. 

*  Helmholtz,  Physiolog.  Optik,  page  345. 


20  PHOTOMETRICAL  MEASUREMENTS 

26.  Physical  basis  of  illumination.  —  Primarily,  illumination 
refers  only  to  the  light  reflected  to  the  eye  from  surrounding 
objects,  yet  for  brevity  it  can  be  taken  to  include  as  well  the 
source  of  light.     The  luminous  source  may  give  out  either 
simple  or  complex  light.     Light  is  simple  when  it  consists  of 
waves  whose  frequencies  lie  within  one  colour  group  alone. 
The  yellow  light  from  an  alcohol  flame  with  sodium  chloride 
in  solution  is  nearly  monochromatic. 

Except  in  such  special  cases  the  quality  of  an  illumination 
is  complex,  containing  all  or  a  part  of  the  colour  groups  of  the 
spectrum  in  varying  amounts. 

In  addition  to  the  frequency  of  each  wave  train,  the  ampli- 
tude of  its  vibration  is  significant.  By  reference  to  Figure  1, 
the  physical  basis  of  illumination  is  seen  to  be  a  function  of 
the  wave  length  X,  and  the  amplitude  pp'  of  its  vibration. 

If  the  experimental  data  are  accepted  as  a  standard  from 
which  the  curves  shown  in  Figure  4  were  platted,  normal  illur 
mination  may  be  defined  as  that  combination  of  frequencies 
and  amplitudes  which  will  excite  the  primary  red,  green,  and 
blue  colour  sensations  to  the  extent  there  indicated. 

27.  The  perception  of  colour. — It  has  already  been  pointed 
out  in  what  sense  a  source  of  light  may  produce  colour  sen- 
sations.     The   colour  sensations   derived  from    non-luminous 
objects,  however,  are  not  produced  so  simply.     In  all  such 
cases  the  illumination  is  due  to  reflected  light,  and  in  this 
process   the  character  of  the  light  undergoes   more   or  less 
change. 

A  white  surface  reflects  practically  all  the  visible  wave 
frequencies  which  fall  upon  it  from  any  source  of  light  what- 
ever. A  coloured  surface,  on  the  other  hand,  suppresses 
certain  frequencies  and  reflects  others ;  a  red  surface  absorbs 
practically  all  wave  frequencies  but  those  corresponding  to  the 
red  colour  groups,  which  it  reflects.  Normal  light  falling  upon 
such  a  surface  is  partially  absorbed  and  partially  reflected, 
while  a  simple  incident  light,  such  as  violet  or  yellow,  is  prac- 


PRINCIPLES   OF   PHOTOMETRY  21 

tically  absorbed  and  the  surface  appears  almost  black.  The 
illumination  of  non-luminous  objects  then,  being  due  to  reflected 
light,  they  require  for  full  illumination  that  the  incident  light 
shall  contain  all  those  wave  frequencies  which  they  can  reflect, 
and  that  the  amplitude  of  the  reflected  waves  shall  be  suf- 
ficiently great  normally  to  excite  appropriate  primary  colour 
sensations  of  the  eye. 

28.  The  duration  of  the  light  impression  upon  the  retina.  —  An 
illumination  impressed  upon  the  retina,  whether  it  is  weak  and 
continued  for  a  long  time,  or  very  intense  and  for  an  exceed- 
ingly short  period,  like  that  of  an  electric  spark,  produces  a 
light  sensation  which  persists  for  a  time  after  the  cause  has 
ceased  to  operate.  The  phenomenon  is  one  of  much  practical 
importance  in  photometry  and  must  be  investigated  in  its 
details  to  determine  in  what  degree  the  length  of  the  period 
of  persistence  is  a  function  of  the  colour,  the  intensity  of  the 
illumination,  and  the  length  of  the  exposure  of  the  retina 
to  it. 

These  details  have  been  carefully  studied  by  Nichols  *  and 
Ferry.  |  They  have  found  that  the  duration  period  shortens 
with  an  increase  of  the  intensity  of  the  illumination  exciting 
the  retina,  and  attains  a  fairly  constant  minimum  value  for  a 
certain  intensity  beyond  which  it  does  not  measurably  lessen. 

The  term  "  duration  period  "  is  not  fully  explicit.  It  defines 
the  length  of  time  over  which  the  sensation  of  light  remains 
sufficiently  strong  not  to  cause  a  rhythmic  variation  when  an 
illumination  is  viewed  through  a  sectored  disk,  rotating  at  a 
critical  speed  for  the  particular  conditions  prevailing.  The 
total  duration  greatly  exceeds  this,  for  such  impressions 
apparently  die  away  by  an  approximately  logarithmic  de- 
crement. 

For  the  duration  period  as  a  function  of  the  intensity  of  the 
illumination,  Ferry  has  obtained  the  values  :  — 

*  E.  L.  Nichols,  American  Journal  of  Science ;  28,  1884,  page  243. 
t  E.  S.  Ferry,  American  Journal  of  Science  ;  44,  1892,  page  192. 


22 


PHOTOMETRICAL   MEASUREMENTS 


Wave 
Length 

Duration  in  Seconds 

0.540 
0.589 
0.684 

0.0200 
0.0170 

0.0192 
0.0161 
0.0238 

0.0172 
0.0147 
0.0217 

0.0156 
0.0132 
0.0192 

16 

0.0133 
0.0102 
0.0172 

24 

0.0199 
0.0081 
0.0156 

The  duration  period  as  a  function  of  the  colour  of  the  illu- 
mination, or  its  prevailing  wave  length,  according  to  Nichols'  * 
experiments,  for  the  brightest  illumination  with  which  he  ex- 
perimented, but  whose  intensity  is  unfortunately  not  stated, 
is:  — 


Colour  and  Wave  Length 
10-7  Millimetre. 

Persistence  Interval 

Length  of  Exposure 

7420  (red) 

0.0769  seconds 

0.00209  seconds 

6463  (orange) 

0.0641       « 

0.00175      " 

6025  (yellow) 

0.0523       " 

0.00144      " 

5415  (green) 

0.0690       " 

0.00188       « 

4784  (blue) 

0.0860       « 

0.00234      « 

4382  (violet) 

0.1072       « 

0.00286       " 

To  determine  the  extent  to  which  the  duration  period  was  a 
function  of  the  length  of  exposure  of  the  retina  to  the  exciting 
light,  the  same  investigator,  employing  a  gas  flame  as  a  light 
source,  found  the  values :  — 


Exposure  of  the  Retina 


Duration  of  the  Image 


0.0124  seconds 

0.0954  seconds 

0.0274   « 

0.0824   " 

0.0717   " 

0.0717   " 

0.1314   « 

0.0654   " 

0.2316   " 

0.0463   " 

0.4506   « 

0.0409   " 

0.7566   « 

0.0327   " 

*  Nichols,  ref.  cit.,  page  247. 


PRINCIPLES   OF   PHOTOMETRY  23 

"  The  effect  of  stimulating  a  '  red,'  '  green/  or  l  violet '  nerve 
is  always  the  sensation  we  call  red,  or  green,  or  violet,  as  the 
case  may  be,  no  matter  what  the  nature  of  the  stimulating 
agent,  and  the  varying  duration  of  colour  impressions  is  due 
primarily  to  variations  in  the  rapidity  with  which  these  nerves 
recover  from  the  action  of  the  impinging  ray.  Of  the  three 
primary  colour  sensations,  green  is  the  most  transient  and 
violet  the  most  persistent.  Upon  this  supposition,  whatever 
may  be  the  predominant  tint  of  a  ray  of  light  under  ordinary 
circumstances,  the  final  impression,  after  the  ray  has  ceased  to 
act,  will  be  one  of  violet. 

"  The  general  conclusions  to  be  drawn  from  these  experiments 
are:  — 

"  (1)  The  persistence  of  the  retinal  image  is  a  function  of  the 
particular  wave  length  producing  it,  being  greater  at  the  ends  of 
the  spectrum  and  least  in  the  yellow  rays. 

"  (2)  It  decreases  as  the  intensity  of  the  ray  producing  the 
image  increases. 

"(3)  The  relative  duration  of  the  impression  produced  by 
the  different  spectral  colours  is  not  the  same  for  all  eyes. 

"  (4)  The  duration  of  the  retinal  image  is  in  inverse  order  to 
the  length  of  exposure  to  a  particular  source  of  illumination."  * 

29.  Talbot's  law.  —  This  very  simple  principle  of  intermit- 
ting the  illumination,  and  diminishing  its  apparent  intensity 
without  affecting  its  quality,  was  stated  by  Talbott  in  1834. 
It  is  practically  the  same  principle  employed  by  Maxwell  in 
his  rotating  disk. 

Accordingly,  when  by  any  suitable  mechanical  means,  the 
light  falling  on  a  surface  is  periodically  cut  off  for  a  very  short 
time  with  a  frequency  which  prevents  the  eye  from  becoming 
conscious  of  the  alternations,  the  effect  on  the  eye  is  equivalent 
to  a  proportionate  decrease  of  the  illumination. $ 

*  E.  L.  Nichols,  ref.  cit.,  page  252. 

t  Philosophical  Magazine  ;  5,  1834,  page  327. 

t  Ladd,  Physiological  Psychology,  page  473. 


24  PHOTOMETRICAL  MEASUREMENTS 

30.  The  rotating  sector  disk.  —  This  principle  is  readily 
applied  in  the  transmission  of  light  by  a  rotating  disk  from 
which  a  sector  has  been  cut  out  for  the  passage  of  the  light. 

The  disk  must  be  rotated 
at  such  a  speed  that  it 
will  make  a  complete 
alternation  within  the 
time  limit  of  the  persis- 
tence of  vision.  Ladd  * 
places  this  at  less  than 
0.04  second.  If  n  is  the 
angular  opening  of  the 
sector  for  the  passage  of 
the  light,  the  illumination 
/  will  be  apparently  re- 
duced to  a  value  /'  such 
that 
FIG.  5.  /' ; 


Or,  in  case  the  disk  (Fig.  5)  is  perforated  with  a  number  of 
sectors,  if  s  is  the  area  of  the  openings  and  S  the  whole  area 
of  the  disk  zone,  then 

I'  =  J/.  (17) 

Such  a  device  is  preferable  to  one  which  diminishes  the  light 
by  absorption,  for  it  does  not  affect  the  quality  or  diminish  its 
intensity,  and  while  it  alters  the  total  amount  of  energy  falling 
on  a  surface  in  a  given  time,  the  effect  of  diminished  sight  sen- 
sation is  wholly  physiological  and  due  to  an  integrating  action 
of  the  eye.t 

*  Ladd,  ref .  cit.  For  time  of  distinct  vision,  consult  Langley,  Ameri- 
can Journal  of  Science  ;  36,  1888,  page  359. 

t  For  an  excellent  discussion  of  the  application  of  the  Talbot  principle, 
see  article  by  Lummer  and  Brodhun,  Zeitschrift  fiir  Instrumentenkunde, 
1896,  page  299. 


PRINCIPLES   OF  PHOTOMETRY 


25 


Ferry  *  has  shown  the  limits  within  which  the  Talbot  prin- 
ciple obtains,  and  has  found  values  for  the  error  in  all  other 
cases  liable  to  occur  in  practice. 

The  relations  pointed  out  by  the  equations  just  stated  are 
physically  true  whatever  the  ratio  of  the  aperture  to  the  disk 

-,  may  be.     But  the  decrease  of  the  physiological  disturbance 

S 

is  not  a  linear  function  of  the  time,  but  the  disturbance  dies 


_\ 


m 


*w\5 


40 


60 


80 


100 


130 


-lift    DEGREES  OF 
ANG.  APERTURE 


FIG.  6. 


out  somewhat  like  damped  vibrations.  When  the  angular 
aperture  of  the  disk  exceeds  180  degrees  the  error  in  applying 
Talbot's  principle  is  negligible,  but  when  it  is  less  than  180 
degrees  the  error  becomes  appreciably  greater  as  the  aperture 
is  diminished,  until  for  24  degrees  it  is  15.6  per  cent  for  the  arc 
light  and  11.3  per  cent  for  the  incandescent  lamp.  The  varia- 
tion of  the  error  with  the  aperture  is  platted  for  each  light  in 
Fig.  6.  It  is  seen  that  the  magnitude  of  the  error  is  affected 
by  the  quality  of  the  light  through  the  greater  persistence  of 


*  Physical  Review,  Vol.  I,  1893,  page  338. 


26          PHOTOMETRICAL  MEASUREMENTS 

the  more  energetic  waves  of  the  less  luminous  end  of  the 
spectrum. 

In  practice  the  errors  due  to  these  complications  may  be  made 
inappreciable  by  not  attempting  to  cut  off  more  than  one-half 
the  incident  light.  The  disk  should  be  rotated  at  a  speed  that 
will  produce  apparently  uniform  illumination  of  the  screen; 
and  any  excess  above  the  critical  speed  for  attaining  this  has 
no  influence  on  the  photometrical  readings. 

31.  The  Purkinje  effect.*  —  The  quality  of  the  sensation  of 
colour  produced  by  an  illumination  is  not  constant  throughout  a 
great  range  of  its  intensity.  As  the  illumination  grows  very 
bright,  all  coloured  surfaces  incline  toward  a  whitish  yellow 
tint,  which  must  gradually  modify  the  quality  of  the  sensation 
appropriate  to  that  particular  colour  of  light.  Purkinje  and 
Dove  seem  to  have  been  the  first  to  discover  that  a  red  surface 
appears  brighter  than  a  blue  one  in  daylight,  while  the  reverse 
occurs  when  these  surfaces  are  viewed  in  weak  daylight.  In 
very  weak  light  the  red  surface  may  even  appear  black,  while 
the  blue  one  will  still  be  visible  in  its  proper  colour. 

In  general,  in  a  bright  light,  red,  yellow,  and  orange-coloured 
surfaces  are  relatively  more  brightly  illuminated  than  blue  and 
violet  ones,  while  just  the  opposite  relations  obtain  in  a  weak 
light.  All  colour  sensations  do  not  then  have  the  same  law  of 
the  variation  of  intensity,  but  each  has  a  different  value  for 
its  rate  of  change,  which  is  much  greater  for  red  than  blue 
illuminations. 

The  Purkinje  effect  is  one  which  must  be  guarded  against 
in  photometry,  except  when  normally  white  illuminations  are 
viewed.  In  case  a  white  screen  or  surface  is  illuminated  from 
a  light  source  of  yellowish  tint,  this  tint  will  be  pronounced 
when  the  surface  is  brightly  illuminated ;  while,  if  the  illu- 
mination becomes  especially  weak,  the  surface  may  assume  a 
bluish  tint. 

*  Purkinje,  Physiologie  der  Sinne,  Vol.  II,  page  109 ;  and  Rood, 
Modern  Chromatics,  page  189 ;  and  Helmholtz,  Physiolog.  Optik,  page  317. 


PRINCIPLES    OF    PHOTOMETRY  27 

This  is  not  without  an  influence  on  the  setting  of  the  screen. 
If  light  sources  of  a  red  or  yellow,  and  a  blue  tint,  as  an  amyl 
acetate  flame  and  an  arc  light,  are  compared  under  the  condi- 
tions of  a  brightly  lighted  screen,  the  photometer  setting  will 
show  a  relative  advantage  in  favour  of  the  red  or  yellow  source. 
Should  the  lights  be  more  widely  separated  until  the  illumina- 
tion of  the  screen  becomes  perceptibly  weak,  the  intensity  of 
the  blue  light  would  be  unduly  emphasized. 


CHAPTER  I 

PHOTOMETRICAL   QUANTITIES 

DEFINITION  OF  FUNDAMENTAL   RELATIONS 

32.  Photometrical  quantities  are  developed  from  the  neces- 
sity for  assigning  dimensions  to  the  physical  relations  involved 
in  any  attempt  at  the  comparison  or  definition  of  the  illumi- 
nating power  of  light  sources.     These  quantities  primarily  deal 
with  the  quantity  of  light,  and  the  distribution  of  its  intensity 
along  radii  vectores,  from  a  luminous  source. 

Luminous  sources  themselves  will  be  considered  in  this 
work  as  either  primary  or  secondary :  a  primary  source  being 
one  which  radiates  luminous  energy  directly  transformed  within 
it  as  the  result  of  the  high  temperature  of  the  source ;  while 
a  secondary  source  is  one  which  reflects  radiant  luminous  energy 
received  upon  it,  or  diffuses  the  energy  passing  through  it. 

33.  Vector  distribution  of  illuminating  power  from  a  primary 
source.  —  For  the  present  discussion  a  primary  source  of  light 
will  be  taken  to  be  a  luminous  sphere  whose  radius  is  negli- 
gibly small  compared  wijh  all  distances  at  which  the  intensity 
is  measured ;   it  may  be  regarded  as  a  point  from  which  the 
light   rays   emanate  with  equal   intensity  along  each  radius 
vector. 

If  about  this  point  as  a  centre,  at  desired  radial  distances, 
concentric  spherical  surfaces  are  supposed  to  be  generated, 
each  such  spherical  surface  will  normally  cut  all  the  rays 
emanating  from  the  luminous  source ;  and  the  total  light  flux 
will  be  the  same  across  each  surface. 

28 


PHOTOMETRICAL   QUANTITIES 


29 


Considering  two  such  spherical  surfaces  Si  and  S2  (Fig.  7) 
with  radii  of  ?\  and  r2  metres,  their  respective  areas  will  be, 

Area  of  Si  =  4  irr?  square  metres,  (18) 

Area  of  S2  =  4  7rr22  square  metres.  (19) 

The  same  quantity  of  light  Q  falls  on  each  surface;  and, 
accordingly,  denoting  the  quantity  of  light  for  each  square  metre 
on  Si  and  S2  by  qi  and  q2, 


and 


Q 


(20) 
(21) 


Consider  further  an  area 
of  m  square  metres  on  each 
spherical  surface  :  the  quan- 
tities of  light  falling  on  these 
areas  from  the  common  source 
will  have  the  relation, 


mql 
mq2 


or 


92    n 


(22) 
(23) 


FIG.  7. 


Should  the  light  not  fall  normally  on  the  spherical  areas 
involved  but  at  an  angle  0,  between  the  normal  to  each  surface 
and  the  path  of  the  light  rays,  the  quantity  of  light  q  will  be, 

Q 


q  — 


cos  0, 


(24) 


while  between  two  parallel  surfaces  mq^  and  mq2  there  will  still 
obtain  the  relation :  —  2 

?!  =  ?«..  (23) 

g2    ^i2 

In  general,  then,  whatever  may  be  the  geometrical  character 
of  areas  illuminated  from  the  same  source,  so  long  as  they  are 
parallel  each  to  each,  the  relations  just  established  may  be 
shown  to  hold  true  for  them. 


30 


PHOTOMETRICAL   MEASUREMENTS 


34.  The  fundamental  law  of  distances. — A  general  law  may 
be  derived  from  these  geometrical  principles,  whatever  may  be 
the  properties  of  the  luminous  source  so  long  as  it  is  practically 
a  radiant  point;  expressed  in  words,  equation  23  reads,  The 
quantity  of  light  falling  on  a  given  surface  varies  inversely  as  the 
square  of  the  distance  from  the  source.  The  working  equation 
derived  from  this  statement  will  be  formally  discussed  in  a 
subsequent  topic  (page  32).  The  geometrical  relations  are 
clearly  shown  in  Figure  8,  for  a  source  of  light  placed  at  L. 


•»^^_ 

*"" 

^^^ 

B 

/ 

/^ 

'-*, 

--v- 

______ 

""^"^.^ 

/ 

~~~       ~~~~~~~~^\ 

_^ 

v*-^^^ 

C                            "~"^~-  -^^=r 

, 

D 

E 

'^^~~~~~*~~~, 

FIG.  8. 

35.  The  intensity  of  illumination.  —  In  order  to  establish  a 
general  statement  of  this  fact,  it  is  seen  from  the  equation,  Q 
being  the  total  quantity  of  light  emitted  by  the  source  at  a 
distance  f  ^ 

(25) 


that  when  q  =  1  with  unit  radius, 


(26) 


From  these  equalities,  a  definition  may  be  derived  which  will 
state  the  intensity  of  illumination  received  on  a  surface  in 
terms  of  a  unit  of  light.  According  to  equation  26  when  the 
radiant  strength  of  the  light  source  is  4  TT  units  of  quantity  of 


PHOTOMETRIC AL  QUANTITIES  31 

light,  a  square  metre  of  the  concentric  spherical  surface  will 
receive  the  unit  quantity  of  illumination,  and  a  light  source  of 
4  Trm  units  of  quantity  of  light  will  produce  on  such  a  surface  a 
quantity  of  illumination  of  m  units.  The  quantity  of  illumina- 
tion on  the  surface  at  unit  distance  is  then  the  measure  of  the 
illuminating  intensity  of  the  light  source. 

If  the  intensity  of  illumination  is  denoted  by  /,  the  quanti- 
ties Q,  /S,  and  0,  being  taken  as  above, 

I  =  |cos0,  (27) 

which  is  the  fundamental  definition  for  the  intensity  of 
illumination. 

In  the  comparison  of  light  sources,  their  intensities  are  con- 
sidered at  various  distances ;  a  light  source  whose  illuminating 
intensity  is  P  units,  as  above  defined,  will,  at  a  distance  of  r 
metres,  show  an  intensity  of  P  units,  following  the  law  of 
distances  ;  the  relations  between  these  three  quantities  are, 

J**-*     I 

-f-        -  (28) 

and  P=/VJ 

36.  The   unit   of   intensity   of   a   light    source.  —  From   the 
equation, 

I=|  (29) 

the  unit  illuminating  intensity  of  the  light  source  is  seen  to 
follow  from  unit  values  for  Q  and  JS.  Then  a  light  source  of 
unit  illuminating  intensity  produces  unit  illumination  of  a  square 
metre  of  concentric  spherical  surface  at  a  radial  distance  of  one 
metre.  The  radiating  strength  of  the  source  is,  however,  4  TT 
units  of  quantity  of  light. 

37.  The   intrinsic  brightness  of  a  light  source.  —  Referring 
again  to  a  light  source  as  a  small  luminous  sphere,  suppose  it 
emits  Q  units  of  quantity  of  light  from  a  light-producing  area 


PHOTOMETRICAL  MEASUREMENTS 


of   U  square  centimetres,  the  intrinsic   brightness  B  of  the 
source  is, 

(30) 


Q 


Or,  the  intrinsic  brightness  of  a  light  source  is  defined  by  the 
quantity  of  light  emitted  for  a  square  centimetre  of  its  area. 

38.  The  generalized  photometrical  law.  —  The  statement  that 
the  quantity  of  light  on  a  given  surface  varies  directly  as  the 
illuminating  strength  of  the  light  source  (equation  25),  and 
inversely,  as  the  square  of  the  distance  from  it,  presupposes 


f 


FIG.  9. 

that  all  compared  surfaces  are  parallel  each  to  each.  It  is 
necessary,  however,  to  pass  from  this  special  case  to  a  perfectly 
general  one,  in  which  the  normals  to  the  surfaces  compared 
may  make  an  angle  with  each  other  or  the  light  rays.  In  Fig. 
9,  SN  is  the  opening  in  a  screen  and  AB  a  section  of  a  lumi- 
nous surface,  and  CD  and  C'D  are  surfaces  illuminated  by  AB. 
If  0  is  the  angle  which  the  normal  to  the  surface  C'D  makes 
with  the  light  rays,  while  the  surface  CD  is  normal  to  them, 
the  illuminated  areas  of  CD  and  C'D,  Sl  and  S&  respectively, 
will  receive  a  like  quantity  of  light  upon  them  and  are  in  the 

relation, 

#!  =  £2  cos  0. 


PHOTOMETRIC  AL   QUANTITIES  33 

The  quantities  of  light  upon  unit  surface  of  each  are, 

?i=  (32) 


and 


Employing  the  values  from  equation  31, 

?2  =  ql  cos  0.  (34) 

The  quantity  of  illumination  received  on  any  given  surface 
thus  varies  directly  as  the  cosine  of  the  angle  of  deviation  of 
its  normal  from  the  paths  of  the  light  rays. 

But  the  quantity  of  light  falling  on  unit  area  is  a  measure 
of  the  intensity  of  illumination  ;  so  in  general,  the  intensity  of 
illumination  /'  on  any  surface  is  related  to  the  normal  inten- 

sity 7,  by, 

J'  =  /cos0.  (35) 

This  important  relation  is  commonly  called  Lambert's  law  of 
the  cosines,  since  it  was  first  enunciated  by  him.*  The  impor- 
tance of  this  law  arises  from  its  application  in  defining  the 
illuminating  power  of  a  light  source  which  in  practice  is  given 
in  the  measure  of  the  intensity  of  the  illumination  of  a 
surface. 

Conversely,  if  the  source  of  light  should  be  the  surface  C'D, 
its  intrinsic  brightness  B'  at  AB  would  have  a  value,  B  being 
the  intrinsic  brightness  normal  to  C'D. 

B'  =  B  cos  0. 

39.  The  nomenclature  of  photometrical  quantities.  —  The  unit 
quantities  which  have  continually  recurred  in  this  discussion 

*  Lambert,  Photometria,  1760.  Consult  Jamin,  Cours  de  Physique, 
III  (3),  page  31.  Also  consult  "  The  Photometry  of  the  Diffuse  Reflexion 
of  Light  on  Matt  Surfaces,"  a  critical  examination  of  Lambert's  law  of 
the  cosines;  II.  R.  "Wright,  Philosophical  Magazine,  February,  1900, 
page  199. 

D        ^, 


34  PHOTOMETRICAL  MEASUREMENTS 

have  been  defined  and  discussed  without  an  attempt  at  their 
designation  by  special  names. 

The  tendency  toward  particular  nomenclature  of  physical 
quantities  has  been  carried  to  a  burdensome  excess  in  many 
cases,  until  it  has  assumed  the  nature  of  scientific  fetichism ; 
and  it  materially  operates  against  the  unity  of  physical  sciences 
and  their  applications. 

With  names  assigned  to  the  fundamental  physical  quantities, 
derived  dimensions  and  units  do  not  call  for  special  designa- 
tion, other  than  such  as  is  physically  descriptive.  Attempts  at 
nomenclature  of  the  photometric  quantities  have  been  made 
notably  by  Hospitalier*  and  Macfarlane.f 


THE  PRACTICAL  UNIT  OF   ILLUMINATING  POWER 

40.  The  candle-power  unit.  $  —  It  has  been  an  almost  uni- 
versal custom  to  refer  the  intensity  of  light  sources  to  that  of 
the  candle  and  to  designate  their  illuminating  property  in  terms 
of  the  candle  power.  The  name  is  consequently  one  originated 
from  custom,  and  not  scientific  practice  and  usage.  The  term 
has  been  generally  used  in  Germany,  England,  and  the  United 
States,  while  in  France  the  standard  of  light  having  been 
chiefly  the  carcel  lamp,  the  light  unit  has  been  called  the 
carcel 

The  origin  of  the  candle-power  unit  is  clearly  indicated  by 
its  name.  When  candles  were  generally  used  for  illumination 
there  was  no  great  variation  in  the  size  of  the  moulds,  and  the 
same  materials  were  commonly  employed  in  making  them  ;  and 
though  there  was  no  apparent  design  about  the  matter,  yet  the 
result  was  there  existed  comparative  uniformity  in  the  char- 
acter of  the  materials,  size  of  wicks,  and  the  finished  candles. 

*  La  Lumiere  Electrique  ;  53,  1894,  page  7. 

t  "Units  of  Light  and  Radiation,"  Transactions  American  Institute 
of  Electrical  Engineers,  1895,  page  85. 

J  W.  M.  S.,  "The  Candle  Power  of  Arc  and  Incandescent  Lamps," 
American  Electrician,  March,  1899,  page  113 ;  and  June,  1899,  page  261 


PHOTOMETRICAL  QUANTITIES  35 

A  candle  flame  much  exceeding  two  inches  in  height  begins 
to  smoke ;  consequently  the  wick  would  be  snuffed  before  the 
flame  attained  a  smoking  height,  and  this  condition,  together 
with  the  close  resemblance  of  candles  wherever  made,  insured 
a  greater  uniformity  of  illuminating  power  from  candles  than 
has  been  obtained  from  any  subsequent  light  source.  It  is  thus 
readily  understood  why  the  candle  came  into  use  as  a  simple, 
concrete  unit  of  light  when  there  began  scientific  comparisons 
of  illuminations  and  light  sources. 

Accordingly,  to-day  we  speak  of  the  measure  of  the  light  of 
an  incandescent  lamp,  arc  lamp,  or  gas  flame,  in  terms  of  the 
candle  power.  Yet  this  adherence  to  the  use  of  an  obsolete 
term  has  more  to  commend  it,  than,  for  example,  the  use  of  the 
foot  as  a  unit  of  length ;  for,  though  the  metric  system  affords 
a  unit  much  superior  to  the  foot,  there  is  as  yet  no  photo- 
metrical  unit  to  displace  the  candle  in  general  acceptance. 

The  action  of  the  American  Institute  of  Electrical  Engineers 
and  of  the  National  Electric  Light  Association  in  giving  official 
indorsement  to  the  opinion  and  usage  of  those  who  have  fully 
investigated  the  subject,  legalizing  the  amyl  acetate  lamp  as 
the  standard  of  illuminating  power,  renders  all  forms  of  can- 
dles obsolete  for  the  light  standard.  Relinquishing  the  candle 
as  the  concrete  light  standard,  should  the  term  "  candle  power  " 
be  retained  ? 

For  illustration :  suppose  the  metre  was  the  generally  legal- 
ized standard  of  length,  and  that  this  action  was  generally 
accepted  and  measurements  were  made  with  metre  sticks  in- 
stead of  foot  rules,  would  it  be  advisable  to  employ  the  ratio  of 
the  metre  to  the  foot,  and  having  made  the  measurements  in 
the  metre  unit,  to  express  the  measured  dimensions  in  feet  ? 

Much  the  same  dilemma  presents  itself  to  photometricians. 
Scientifically  and  legally,  candles  are  no  linger  in  repute,  and 
the  amyl  acetate  standard  is  the  accepted  unit  of  light.  Shall 
a  ratio,  then,  even  if  it  were  possible  to  obtain  it,  between  the 
amyl  acetate  lamp  and  the  candle  be  employed,  and  all  deter- 
minations of  the  light  strength  of  illuminating,  sources  made 


36  PHOTOMETRICAL   MEASUREMENTS 

against  the   amyl   acetate   standard   be   finally  expressed   in 
candle  power  terms  ? 

The  numerous  candle  power  ratings  of  the  standard  candle 
in  the  literature  of  photometry  are  only  mean  values  obtained 
between  wide  extremes,  or  merely  figures,  and  represent  no  phy- 
sical quantity.  The  term  "  candle  power,"  then,  being  mean- 
ingless as  a  quantitative  expression,  and  the  amyl  acetate  lamp 
being  fairly  precise  as  a  standard  light,  photometricians  might 
follow  the  example,  notably  of  German  practicians,  and  ex- 
press illuminating  power  in  terms  of  Hefner  units  (Hefner 
Licht  is  the  current  term  in  Germany). 

A  reasonable  objection  to  such  a  procedure  is,  that  a  change 
once  made,  a  better  light  standard  than  the  amyl  acetate  lamp 
might  be  introduced  and  the  necessity  would  arise  for  a  second 
revision  of  the  name  of  the  light  unit ;  and  so  on  indefinitely. 
Eef erring  again  to  the  analogy  between  this  subject  and  the 
metre  as  a  standard  of  length,  it  may  be  advanced  that  the 
metre  is  a  purely  arbitrary  standard  of  length,  though  it  was 
designed  to  be  an  absolute  one,  and  for  similar  reasons  the  can- 
dle power  may  be  retained  as  an  arbitrary  light  unit  both  in 
name  and  assigned  value.  The  analogy  is  only  apparent,  for 
there  can  exist  no  material  representation  of  the  candle  power 
unit  of  light,  since  it  is  an  indeterminate  quantity.  Candle 
power  is,  then,  a  mere  name  corresponding  to  no  physical  quan- 
tity, and  in  the  adoption  of  the  Hefner  unit  along  with  the 
material  amyl  acetate  standard  there  is  in  reality  nothing  to 
relinquish  but  a  custom. 

According  to  established  scientific  precedents  there  is  no  in 
consistency  in  naming  the  unit  of  light  after  an  individual 
connected  with  its  development.  This  custom,  now  seemingly 
well  established,  is  at  best  a  questionable  one.  The  more 
rational  procedure  would  be  that  followed  with  reference  to 
heat.  A  quantity  of  heat  is  expressed  in  terms  of  Heat  Units 
or  British  Thermal  Units. 

Applying  this  to  the  present  discussion,  the  term  "candle 
power  "  as  well  as  personified  terms  might  reasonably  be  aban- 


PHOTOMETKICAL   QUANTITIES  37 

doned  and  the  illuminating  power  of  light  sources  be  expressed 
simply  in  Light  Units.  As  the  science  of  light  standards  ad- 
vances and  the  light  strength  of  actual  standards  becomes  ex- 
pressible with  very  great  precision,  the  term  "  Light  Unit  "  will 
apply  with  equal  force.  If  the  value  of  the  light  unit  is 
changed  by  the  action  of  a  congress  or  other  body,  it  will 
cause  no  more  confusion  than  was  occasioned  by  the  change  in 
the  value  of  the  heat  unit  by  a  redetermination  of  the  mechan- 
ical equivalent  of  heat. 

The  unit  for  expressing  the  quantity  of  a  phenomenon  must 
be  of  the  same  character  as  the  thing  measured  ;  and  this  unit 
value  can  be  no  more  precise  than  the  value  of  the  thing  meas- 
ured. As  the  measurement  of  the  phenomenon  grows  more 
and  more  precise,  to  that  .extent  will  the  value  of  the  unit  be- 
come definite. 

41.  The  candle-power  unit  of  illumination  is  the  illumination 
received  on  a  concentric  spherical  surface  of  one  square  metre  in 
area  at  a  radial  distance  of  one  metre  from  a  source  of  light 
whose  intensity  is  one  candle  power. 

Denoting  the  intensity  of  the  illumination  by  /, 

I=%  (36) 

where  Q'  is  the  amount  of  light  falling  on  a  spherical  surface 
of  AS"  square  metres  ;  and  a  general  expression  for  intensity  of 
illumination  in  terms  of  the  candle  power  (C.  P.)  of  the  source 
and  at  a  radial  distance  R  metres  is, 


the  result  being  expressed  in  terms  of  the  candle-metre. 

For  the  average  eye,  ordinary  print  may  be  easily  read  with 
an  illumination  of  4  to  6  candle-metre  units  of  intensity  which 
at  a  distance  of  two  metres  corresponds  to  a  light  source  whose 
illuminating  power  is  16  to  24  candles. 


38 


PHOTOMETEICAL  MEASUREMENTS 


MEAN  SPHERICAL  INTENSITY 

42.  The  theory  of  the  subject  will  first  be  considered  and 
that  from  a  geometrical  standpoint.  In  Figure  11,  0  is  the  cen- 
tre of  the  polar  coordinates  along  which  certain  radial  distances 
are  platted,  while  the  curve  joining  their  extremities  has  a  con- 
tour somewhat  resembling  the  distribution  of  the  luminous  in- 


iO" 


80°  80e 

FIG.  10. 


00° 


tensity  about  an  alternating  current  arc.     The  problem  is  to 
find  the  mean  radial  distribution  about  the  centre  0. 

Considering  the  case  shown  in  Figure  10,  wherein  the  curve 
is  a  circle  OMN  whose  periphery  passes  through  0  tangent  to 
the  vertical  coordinate  TOS,  the  polar  equation  to  such  a 


curve  is 


r  =  2  a  cos  0, 


(38) 


./ 

r-s   V^HOTOMETRICAL  QUANTITIES  39 

a  =  ^OP  being  the  constant  radius  of  the  curve  and  r  the 
variable  distance  along  the  polar  coordinates  from  0  to  the 
periphery  of  the  circle  OMN. 

The  area  included  by  the  circular  curve  is  found  by  double 
integration  of 

A  =  area  circle  =  2  f  f  C\dff)(rdf).  (39) 

«/0     c/0 

It  is  to  be  observed  that  the  law  of  the  variation  of  the  distance 
from  the  centre  0  to  the  curve  is  known,  and  this  distance 
is  a  continuous  function  of  the  inclination  to  the  polar  axis. 
Similarly,  in  all  cases  in  which  the  radial  distance  is  known 
to  be  a  continuous  function  of  the  inclination  the  area  in- 
cluded in  the  curve  may  be  found.* 

Further,  it  is  supposed  that  the  circle  is  a  section  through  a 
figure  of  revolution  about  the  vertical  coordinate  TOS  as  an 
axis ;  and  it  is  desired  to  find  the  dimensions  of  an  equivalent 
sphere  whose  radius  shall  be  the  mean  radius  of  the  figure 
of  revolution.  -The  section  of  the  figure  of  revolution  taken 
through  the  axis  TOS  would  show  two  equal  circles  OMN  and 
OM'N',  having  each  the  area  A  as  found  by  equation  39. 

The  section  through  the  equivalent  sphere  having  the  centre 
0  in  common  with  the  figure  of  revolution  will  be  a  circle  whose 
area  is  2A,  the  area  of  the  section  of  the  figure  of  revolution. 
The  radius  r1  of  the  mean  sphere  is  then  readily  found,  and  is 

(40) 

In  the  figure  the  area  of  the  circle  EFGH  is  taken  as  double 
the  area  of  OMN  and  represents  a  prime  section  through  the 
mean  sphere,  and  EO  is  thus  the  mean  spherical  radius  of  the 
equivalent  of  the  figure  of  revolution. 

When  the  equation  to  the  curve  can  not  be  stated,  or  rather 

*  Consult  Murray,  Integral  Calculus,  Chapter  IX,  for  a  discussion  of 
the  area  included  by  a  polar  curve. 


40 


PHOTOMETRICAL   MEASUREMENTS 


the  radial  distance  is  not  a  continuous  function  of  the  inclina- 
tion, the  area  can  not  be  integrated  by  purely  mathematical 
processes,  and  recourse  must  be  had  to  mechanical  integration. 
This  may  be  done  either  by  a  planimeter  or  a  graphical  con- 
struction. 

80°  80°  60° 


60 


40 


y 


\ 


\ 


30 


X 


40 


20 


30 


40° 


60 c 


80° 


80° 


60C 


FIG.  11. 


The  four  loops  in  Figure  11  are  such  an  instance,  and  represent 
a  distribution  which  is  different  in  each  of  the  four  quadrants. 
In  this  figure,  the  area  bounded  by  the  curved  contour  and 
the  rectangular  axes  is  found  for  each  quadrant,  and  the 
sum  of  these  areas  is  equated  to  the  prime  section  of  the 


PHOTOMETKICAL  QUANTITIES  41 

equivalent  mean  sphere,  the  radius  of  which  is  then  found 
by  the  equation: 

/V  A 

(41) 

THE  PRACTICE  OF  THE  MEAN  SPHERICAL  INTENSITY 

43.  It  is  evident  that  the  light  source  which  has  been  as- 
sumed—  a  small  equably  luminous  sphere  —  is  not  met  with  in 
practice.  With  the  incandescent  lamp,  the  light  source  is  a 
looped,  luminous  filament,  and  the  base  of  the  lamp  prevents 
the  emission  of  light  in  that  direction.  With  the  arc  lamp,  the 
distribution  of  light  varies  widely  with  the  type  and  in  all 
cases  shows  marked  irregularity.  Similar  conditions  exist  with 
gas  flames  and  incandescent  gas  mantles.  Also  the  distribution 
of  the  emitted  light  is  again  profoundly  varied  by  the  use  of 
reflectors,  and  enclosing  chambers  and  globes.  (Appendix  A.) 

These  irregularities  of  distribution  render  it  difficult  to 
specify  the  illuminating  power  of  any  of  these  light  sources  in 
general  terms;  and  the  comparison  of  one  light  source  with 
another  is  no  less  difficult  and  ambiguous.  This  subject  is  at 
once  both  scientifically  interesting  and  of  great  practical  im- 
portance. 

The  light  distribution  (see  Fig.  50,  page  196)  about  an  incan- 
descent filament  is  a  function  of  its  cross  section  and  the  form 
of  the  loop.  To  express  its  illuminating  power  with  accuracy, 
the  radial  direction  along  which  it  is  specified  must  be  noted, 
whether  it  is  horizontal,  vertical,  or  at  a  given  angle  of  incli- 
nation to  the  horizontal  plane  through  the  filament ;  and  the 
azimuth,  too,  must  be  given.  Incandescent  lamps  having  fila- 
ments of  different  shapes  cannot  be  directly  compared,  for 
their  light  distribution  is  not  similarly  intense  along  a  speci- 
fied vector  or  radius. 

The  light  distribution  about  the  open  arc  of  a  continuous 
current  lamp  is  notably  deformed  from  a  spherical  one ;  nor  is 
the  distribution  constant,  for  it  varies  from  time  to  time,  as 


42  PHOTOMETRICAL  MEASUREMENTS 

the  carbon  tips  burn  to  a  new  shape.  It  also  varies  with  the 
size  and  quality  of  the  carbons  burned.  So  irregular  is  the 
distribution  that  the  statement  of  the  illuminating  power  of 
a  given  arc  is  without  significance  unless  it  is  stated  along  a 
specified  vector.  The  problem  increases  in  complexity  and  un- 
certainty as  the  arc  lamp  considered  is  of  the  alternating  cur- 
rent type  or  is  an  enclosed  arc.  The  case  is  similar  for  gas 
flames  of  different  types  and  is  here  further  complicated  by 
reflectors. 

The  practical  applications  of  these  varied  light  sources  as 
well  as  their  scientific  uses  render  a  system  imperative  for  the 
specification  of  illuminating  power  and  comparison  of  illumi- 
nating intensity.  The  theory  of  such  a  system  has  been  stated 
and  it  now  remains  to  point  out  its  applications. 

The  arc  lamp  being  so  pronounced  in  the  peculiarities  of  its 
light  distribution,  will  alone  be  considered  in  this  discussion; 
for  any  light  source  whatever  may  be  similarly  investigated. 

In  Figure  11  is  shown  a  distribution  of  luminous  intensity 
about  an  alternating  current  arc ;  and  while  the  distribution  is 
not  strictly  a  figure  of  revolution,  or  symmetrical  about  any  axis, 
the  curve  shown  is  the  distribution  on  a  vertical  plane  through 
the  arc  centre,  and  will  be  considered  as  an  average  of  all  simi- 
lar plane  distributions. 

The  method  for  obtaining  such  curves  will  be  subsequently 
discussed  (see  pages  216  and  236). 

The  maximum  intensity  here  exceeds  800  units,  and  the  mini- 
mum is  less  than  400.  The  areas  of  the  curves  in  the  four 
quadrants  were  found  to  be,  using  a  planimeter, 

Quadrant  1 4.8  square  inches. 

"2 5.0        "          " 

"3 6.1        "          " 

«         4 5.8       "          « 

yielding  a  total  area  included  by  the  curved  contour  of  21.7 
square  inches.  This  area  was  equated  to  the  area  of  a  prime 
section  of  an  equivalent  sphere,  whose  radius  was  found  to  be 


PHOTOMETKICAL  QUANTITIES  43 

2.63  inches.  This  circle  being  now  considered  as  a  section  of 
a  figure  of  revolution,  it  defines  the  equivalent  mean  spherical 
distribution  of  the  light;  and  the  radius  of  this  equivalent 
sphere  is  2.63  inches.  Eeferring  this  dimension  to  the  scale  on 
which  the  curve  was  platted,  the  mean  spherical  intensity  is 
found  to  be  526  units. 

The  meaning  of  this  quantity  is  obvious:  If  the  flux  of 
light  across  the  actual  surface  about  the  arc  0,  of  which  the 
curve  is  a  plane  section,  was  uniformly  distributed  over  an 
equivalent  spherical  surface,  this  surface  would  be  one  of  mean 
value  for  the  flux,  and  the  radial  intensity  would  be  the  mean 
spherical  intensity  desired. 

In  a  similar  manner,  if  the  light  flux  indicated  by  the  curve 
in  any  one.  quadrant,  such  as  1,  2,  3,  or  4,  is  alone  considered, 
the  area  between  the  contour  and  the  axes  may  be  taken  and 
equated  to  the  area  of  an  equivalent  circle,  and  the  radius  of 
this  circle  will  be  that  from  which  the  equivalent  mean  spheri- 
cal intensity  of  this  quantity  of  light  from  the  arc  0  can  be 
found.  Or,  any  two  quadrants  may  be  considered  at  pleasure, 
and  the  mean  spherical  intensity  of  the  quantity  of  light  which 
they  represent  may  be  accordingly  determined. 

44.  The  mean  hemispherical  intensity. — A  second  aspect  may 
be  given  to  the  method :  Suppose  that  the  light  flux  indicated 
by  the  curves  in  quadrants  3  and  4,  Fig.  11,  is  considered  only 
with  reference  to  the  light  distribution  below  the  horizontal 
plane  through  the  arc  0,  the  sum  of  the  areas  included  be- 
tween the  curves  and  the  axes  of  the  quadrants  3  and  4  is 
equated  to  an  equivalent  semicircular  area,  and  the  radius  is 
found  as  before.  By  means  of  this  radius  the  mean  hemi- 
spherical distribution  is  defined,  which  in  the  case  platted 
amounts  to  550  intensity  units.  This  lower  mean  hemispheri- 
cal intensity  is  greater  than  the  mean  spherical  intensity  tak- 
ing the  four  quadrants  into  account,  since  the  flux  of  light  over 
the  space  below  the  horizontal  plane  is  in  excess  of  that  above 
it,  as  is  shown  by  the  curves. 


44 


PHOTOMETRICAL  MEASUREMENTS 


A  better  defined  case  is  shown  in  Figure  12;  the  light  distri- 
bution was  platted  only  over  the  section  below  the  horizontal 
plane  through  the  arc  0.  The  areas  included  are, 

Quadrant  3 6.55  square  inches. 

«         4  6.65        "        " 


Their  combined  area  of  13.2  square  inches  is  equivalent  to 
the  area  of  a  semicircle  of  2.9  inches7  radius,  which  scaled,  de- 
fines the  mean  hemispherical  intensity  of  580  units. 

In  the  general  consideration  of  continuous  current  arcs,  the 
mean  hemispherical,  rather  than  the  mean  spherical  intensity 
is  of  value,  for  the  illumination  of  such  an  arc  is  utilized  in  the 
horizontal  plane  and  below  it. 

It  is  obvious,  however,  that  the  mean  spherical  and  hemi- 
spherical values  have  but  little  practical  bearing  on  questions 
of  illumination  in  general.  For  the  specific  illumination  of  an 
object  or  for  illumination  in  any  specific  direction,  the  actual 
intensity  in  such  direction  is  the  important  quantity  to  be  de- 
termined ;  but  for  the  complete  comparison  of  one  light  source 
with  another,  and  for  ascertaining  the  efficiency  of  any  light 
source,  the  mean  spherical  value  must  be  considered. 


CHAPTER   III 

PHOTOMETERS 

THE  ELEMENTS  OF  THE  PHOTOMETER 

45.  ANY  comparable  or  measurable  effect  of  light  may  be 
taken  as  a  basis  for  photometry,  and  an  apparatus  designed  for 
utilizing  it.  From  time  to  time  a  large  number  of  photom- 
eters, employing  various  effects  of  light,  and  embodying,  per- 
haps, only  a  slight  modification  of  some  previous  form,  have 
been  proposed,  and  certain  of  these  have  proven  their  prac- 
tical worth. 

The  attempt  to  trace  the  historical  development  of  the 
photometer,  and  to  describe  the  various  forms  which  it  has  in 
turn  assumed,  belongs  rather  to  the  physical  treatise  on  the 
subject,  and  could  not  be  adequately  discussed  within  pre- 
scribed limits,  and  would  appeal  to  the  investigator  rather 
than  the  practician. 

The  present  tendencies  in  photometry  are  toward  a  develop- 
ment of  the  light  standard,  and  of  standard  conditions  of 
illumination;  for  the  sensitiveness  and  adaptability  of  avail- 
able apparatus  for  the  comparison  of  lights  are  now  greatly  in 
excess  of  the  reliability  of  the  standard  of  light. 

The  present  discussion  will  be  confined  especially  to  certain 
photometers  which  have  a  demonstrated  practical  value,  and 
to  certain  principles  of  design  which  are  favourable  for 
further  modifications ;  and  to  a  brief  historical  outline  of  the 
development  of  the  photometer  into  approved  forms.  The  gas 
lighting  industry  has  been  the  occasion  for  the  proposal  and 
introduction  of  a  very  large  number  of  types  of  the  photometer, 

45 


46  PHOTOMETRICAL  MEASUREMENTS 

and  those  which  have  not  proven  useful  in  the  photometry  of 
electric  lights  will  be  omitted,  as  they  do  not  properly  find  a 
place  in  this  work. 

46.  The  photometer  defined.  —  The  term  "  photometer  "  will 
be  used  in  this  discussion  with  a  restricted  meaning.     As  ordi- 
narily employed  the  word   applies   to  the  entire  apparatus, 
simple  or  complicated,  which  is  especially  designed  for  meas- 
uring the  relative  intensities  of  luminous  sources,  and  thus 
includes  the  bench  or  mounting,  the  observing  screen,  and, 
possibly,  the  standard  of  light  and  other  accessories.     In  a 
broad  sense  no  exception  can  be  taken  to  this ;  but  in  a  work 
devoted  to  the  measurement  of  illuminating  sources  it  becomes 
necessary  to  discriminate  and  insist  upon  rather  narrow  clas- 
sifications, which,  sharing  the  character  of  restricted  classifi- 
cation in  general,  may  often  become  arbitrary. 

The  act  of  measurement  involved  in  photometry  is  confined 
to  observations  of  the  illumination  of  the  lights  compared  upon 
some  form  of  screen ;  and  taking  this  as  a  basis,  the  photometer 
is  the  screen  and  its  accessories. 

In  the  photometrical  train  of  apparatus  the  standard  of  light 
is  the  fundamental  feature,  and  its  importance  is  so  great  that 
it  demands  a  very  considerable  discussion.  A  working  standard 
being  available,  the  next  essential  feature  is  the  photometer  or 
a  suitable  observing  and  comparing  apparatus. 

47.  The  photometer  consists   in  all   its  modifications  of  a 
screen,  which  is  a  device  for  receiving  the  illumination  from 
the  light  sources  compared ;  it  may  have  in  addition  a  contain- 
ing case,  or  mounting,  with  an  ocular  aperture  or  an  observing 
telescope ;  and  the  whole  may  be  fitted  to  some  form  of  carriage, 
or  ways,  if  movable,  for  setting  it  at  certain  points  along  a  bar 
or  guide,  which  forms  a  part  of  what  will  be  called  the  bench. 

48.  The  photometer  bench,  as  its  name  indicates,  is  a  device 
for  mounting  the  lights  compared  and  the  photometer,  and  is 
fitted  with  appropriate  scales.     The  bench  proper  may  consist 


PHOTOMETERS  47 

of  bars  or  rails,  which  form  a  track  for  the  two  carriages 
mounting  the  lights  under  comparison  and  the  photometer 
carriage ;  or  it  may  be  a  simple  base  fitted  with  guides,  and  in 
any  case  some  form  of  scale  is  attached  or  marked  on  it  for 
indicating  the  respective  distances  between  the  screen  and  the 
lights.  In  some  forms  the  photometer  is  stationary,  while  the 
lights  are  movable  along  ways.  In  a  few  apparatuses  of  com- 
pact form,  the  bench  becomes  a  containing  case  for  the  other 
members. 

49.  The  screen.  —  In  their  operation  screens  either  reflect  or 
diffuse   the  illuminations  under  comparison.      They  may  be 
observed  directly  by  the  unaided  eye  or  through  the  agency  of 
some  optical  train. 

50.  The  reflecting  screen  acts  by  irregular  and  not  specular 
reflection.     The  specular  reflection  from  the  plane  surface  of  a 
mirror  or  its  equivalent  would  produce  an  image  of  the  source 
of  the  light  in  the  eye  with  diminished  brightness,  and  no 
effect  from  which  the  illumination  caused  by  the  light  could 
be  observed. 

In  photometry  the  illumination  caused  by  a  light  is  the 
quantity  directly  investigated,  and  the  brightness  of  the  light 
producing  it  is  derived  by  inference. 

The  surface  of  the  reflecting  screen,  then,  must  be  finely  and 
uniformly  grained  in  order  to  scatter  the  light  regularly  inci- 
dent upon  it ;  yet  the  grain  must  not  be  so  marked  that  it  will 
be  distinctly  visible.  Such  a  surface  reflects  the  light  irregu- 
larly, and  the  light  effect  on  the  eye  is  that  of  illumination, 
filling  the  eye  with  light  and  not  with  an  image  of  the  light 
source  (page  8). 

The  light  reflected  from  the  screen  will  always  be  diminished 
in  amount,  and  may  of  may  not  be  materially  changed  in  qual- 
ity. The  sensitiveness  increases  in  proportion  as  the  loss  of 
light  by  reflection  is  diminished. 

The  principle  of  selective  absorption  is  occasionally  utilized 
in  screens,  when  by  the  use  of  an  appropriately  coloured  surface 


48  PHOTOMETRICAL  MEASUREMENTS 

the  light  is  modified  in  its  reflection  to  agree  in  colour  with  the 
compared  light. 

Paper  is  a  frequently  used  material  for  the  screen,  while  ex- 
cellent ones  are  made  from  finely  grained  plaster  of  Paris  or 
from  magnesium  oxide  or  carbonate,  and  similar  substances. 
All  screens  of  this  class  diffuse  the  incident  light  by  reflec- 
tion. 

51.  Diffusing  screens  are  distinguished  from  the  preceding 
class  by  their  property  of  scattering  the  light  in  its  transmis- 
sion through  them.  They  are  made  from  some  translucent 
substance,  and  of  sufficient  thickness  to  prevent  the  image  of 
the  light  source  from  being  formed  in  the  eye.  In  their  opera- 
tion these  screens  always  reduce  the  intensity  of  the  light,  and 
they  may  be  designed  to  change  materially  its  quality  by 
selective  absorption. 

The  sensitiveness  of  diffusing  screens  is  dependent  upon  the 
extent  to  which  they  are  translucent.  Their  translucence  may 
be  due  to  one  of  several  causes.  The  screen  may  consist  of  a 
transparent  matrix,  such  as  a  layer  of  gelatine,  or  celluloid, 
having  uniformly  mixed  through  it  some  finely  divided  solid. 
The  light  in  passing  through  such  a  film  is  reflected  from  the 
surface  of  one  small  particle  to  another,  issuing  after  a  large 
number  of  such  reflections  in  a  diffused  state.  A  large  part  of 
the  light  is  necessarily  absorbed  in  the  process,  it  being  dimin- 
ished to  a  certain  extent  by  each  reflection  in  the  series.  Screens 
of  this  character  are  not  highly  sensitive  and  are  apt  to  change 
the  quality  of  the  light  in  its  passage  through  them.  Opal 
glass  is  a  variety  against  which  this  objection  is  especially 
urged. 

A  second  method  for  making  a  translucent  screen  depends 
upon  the  multiple  reflection  of  the  light  from  a  great  number 
of  small  surfaces,  by  the  method  of  total  reflection  at  the 
bounding  layers  between  two  media  of  different  densities.  The 
translucence  of  the  foam  from  a  transparent  liquid  is  caused  in 
this  manner. 


PHOTOMETERS  49 

52.  Materials  for  translucent  screens.  —  This  character  of 
screen  possesses  such  excellence  that  it  has  been  successfully 
employed  in  a  number  of  important  investigations,  especially 
by  Violle.*  It  should  be  carefully  considered  by  the  photom- 
etrician,  as  it  is  capable  of  many  useful  applications. 

Serviceable  screens  of  the  tissue  variety  may  be  made  from 
thin  paper  of  fine  texture,  preferably  such  as  is  not  calendered 
and  filled  with  earthy  materials.  Their  sensitiveness  may  be 
increased  by  treatment  with  any  preparation  which  will  render 
them  more  translucent  without  causing  them  to  become  trans- 
parent. Very  thin  tracing  cloth  being  of  a  similar  nature  may 
also  be  used  to  advantage.  Formerly  very  thin  shavings  of 
horn  were  considered  to  make  good  screens.  The  sensibility 
of  this  variety  of  screens  is  low,  and  they  are  not  adapted  for 
work  requiring  great  refinement  in  the  observations,  though 
they  may  prove  satisfactory  in  ordinary  practice. 

Opal  glass,  though  seemingly  a  suitable  material  for  a  screen, 
should  be  avoided.  Its  opalescence  is  caused  by  very  finely 
divided  solids  suspended  in  the  sheet  of  clear  glass.  Owing 
to  the  fineness  of  these  particles,  they  perceptibly  change  the 
quality  of  light  passing  through  the  glass  until  it  assumes  a 
reddish  yellow  tinge.  The  particles  are  sufficiently  large 
to  reflect  back  and  dissipate  the  violet  rays,  but  are  too  small 
to  affect  the  slower  rays  toward  the  red  end  of  the  spectrum  to 
any  considerable  extent. f  These  strictures  apply  equally  to 
opalescent  celluloid  films  or  other  films  containing  suspended 
solid  matter. 

Transparent  sheets  having  a  matt  surface  imparted  by  grind- 
ing or  etching  are  not  to  be  confused  with  the  opalescent 
screens.  They  owe  their  translucence  to  a  surface  broken  up 
into  very  minute  grains  or  elevations  having  bright  surfaces, 
which  are  good  reflectors  and  diffuse  the  light  without  change 
in  quality  and  with  comparatively  little  loss.  An  objection  is 
urged  against  these  screens,  that  they  soil  readily,  and  the  sur- 

*La  Lumiere  Electrique  ;  34,  page  52. 

t  See  Tyudall,  Heat  as  a  Mode  of  Motion,  page  483. 


50  PHOTOMETRICAL  MEASUREMENTS 

face  once  injured  by  dirt  or  grease  can  not  be  restored.  How- 
ever, with  proper  treatment  the  diffusing  power  of  the  surface 
can  be  almost  wholly  restored.  Films  of  matt  celluloid,  while 
not  so  durable  as  ground  glass,  yet  give  good  service  and  are 
fairly  sensitive. 

The  most  sensitive  screens  are  those  in  which  transparent 
substances  of  different  densities  are  combined.  Foucault* 
used  a  thin  layer  of  milk  dried  on  plate  glass.  Thin  starch 
water  dried  on  glass,  too,  answers  a  good  purpose.  Crova  ob- 
tained the  best  screens  by  using  beet-root  starch,  which  is 
characterized  by  very  small  spherical  granules  of  great  trans- 
parency. 

53.  The  sensitiveness  of  a  screen  depends  directly  upon  its 
luminous  efficiency  determined  by  the  ratio  of  the  light  deliv- 
ered, to  the  incident  light. 

The  sensitiveness  of  the  photometer  setting  is  ultimately  de- 
termined by  the  magnitude  of  the  least  light  change  which  is 
visible  to  the  observer,  which  may  vary  from  -^  of  the  total 
illumination  when  this  is  weak,  to  y^-  or  even  less  when  it 
is  bright.!  Whatever  this  least  change  may  be  for  the  par- 
ticular observer  and  observation,  the  vision  can  not  be  rendered 
more  acute  by  any  amplifying  instrumental  means. 

The  criterion  for  the  sensitiveness  of  the  screen  demands  that 
it  shall  deliver  to  the  eye  a  sufficiently  brilliant  illumination  to 
enable  the  eye  to  distinguish  the  normal  visual  difference,  say 
the  y^-jj-  part.  That  the  screen  may  accomplish  this  associated 
with  very  great  sensitiveness  in  the  setting,  it  is  essential  that 
the  compared  lights  be  separated  to  a  considerable  distance. 
For  a  screen  of  low  optical  efficiency  to  satisfy  the  criterion  for 
sensitiveness  it  is  necessary  to  place  the  compared  lights  close 
together,  a  proceeding  which  reduces  the  sensitiveness  of  the 
settings,  with  a  resulting  wide  limit  of  uncertainty  in  the  pho- 

*  Crova,  Annales  de  Chimie  et  de  Physique,  Ser.  6,  VI,  page  342  ;   an 
excellent  description  of  such  screens, 
t  Helmholtz,  Physiolog.  Optik,  page  328. 


PHOTOMETERS  51 

tometrical  values  measured.  To  remedy  this  latter  fault,  screens 
of  greater  optical  efficiency  must  be  used  that  the  lights  may  be 
worked  at  a  greater  separation.  Whatever  design  the  screen 
may  assume,  it  is  theoretically  satisfactory  with  a  given  separa- 
tion of  the  lights  so  long  as  it  transmits  a  sufficiently  brilliant 
illumination  for  acute  vision,  and  one  screen  is  superior  to 
another  within  such  limit  only  so  far  as  it  has  some  provision 
for  sharply  defining  the  boundaries  of  the  illuminated  fields 
compared. 

54.  The  Inclination  of  the  Screen.  —  Generally  screens  are  so 
placed  that  the  light  falls  upon  them  along  the  normal  to  their 
surface.     But  the  illumination  of  the  screen  may  be  varied, 
providing  the  surface  is  regular,  by  inclining  it  to  the  photo- 
metrical  axis,  instead  of  changing  the  distance  from  the  light 
source  (page  32).     If  Q  is  the  total  light  falling  upon  the 
screen,  and  a  its  coefficient  of  reflection,  and  0  the  angle  of 
inclination  of  its  normal  to  the  photometrical  axis,  the  reflected 
lightQ' will  be  Q,  =  aQcos,.  (42) 

An  application  is  made  of  this  in  a  few  photometers,  and  to 
some  extent  in  arc-light  photometry.  When  the  screen  has  an 
uneven  surface,  such  as  rough-grained  drawing  paper,  this  law 
is  not  closely  followed. 

55.  A  classification  of  screens.  —  This  part  of  the  apparatus  is 
variously  modified  in  different  types  of  photometers,  and  in 
some  cases  is  combined  with  more  or  less  complex  optical  de- 
vices for  the  purpose  of  comparing  the  diffused  illuminations 
from  the  light  sources.     Kegarding  their  action,  screens  may 
be  divided  into  two  general  classes. 

The  Simple  Screen  is  characterized  by  a  surface  from  which 
the  light  from  the  luminous  sources  under  comparison  may  be 
reflected  in  a  diffused  state  that  it  may  be  viewed  by  the  eye  as 
an  illumination ;  or  is  a  film,  sheet,  or  plate,  which  similarly 
diffuses  the  light  from  the  sources  in  its  passage  through  it. 


52          PHOTOMETRICAL  MEASUREMENTS 

TJie  Compound  Screen  is  one  whose  action  depends  upon 
diffuse  reflection  from  the  surface,  combined  with  transmission 
through  a  translucent  portion.  Such  a  screen,  for  instance, 
characterizes  the  Bunsen  photometer. 

THE   BOUGUER  PHOTOMETER* 

56.  This,  said  to  be  the  oldest  form  of  apparatus  devised 
for  comparing  the  intensities  of  luminous  sources,  was  con- 
structed by  Bouguer  prior  to  1760.  f  It  is  naturally  the  first 


S 
FIG.  13. 


device   that  would   suggest   itself   to   one   seeking  to   apply 
Kepler's  law  of  the  inverse  squares. 

The  compared  lights  S  and  P  (Fig.  13)  are  placed  in  front 
of  an  opaque  reflecting  screen,  AB,  so  that  they  illuminate  it 
normally  to  its  surface.  A  blackened  partition  TN  divides  the 

*  Essai  d'Optique,  1729 ;  also  Traite*  d'Optique  sur  la  gradation  de  la 
lumiere ;  Paris,  1760. 

t  Bouguer  died  in  1758,  though  his  work  announcing  the  photometer  was 
not  published  until  1760.  The  date  of  the  publication  of  this  work  on 
optics  has  been  confused  by  some  with  that  of  the  construction  of  the 
apparatus. 


PHOTOMETERS  53 

screen  into  two  equal  portions  and  extends  outward  normally 
from  the  screen  to  such  a  distance  that  none  of  the  light  from 
one  source  shall  fall  on  the  opposite  half  of  the  screen.  The 
lights  were  moved  perpendicularly  to  the  screen  to  obtain  an 
equality  of  the  illuminations.  The  distances  of  the  lights  S 
and  P  from  the  screen  being  respectively  I  and  L,  the  law  of 
inverse  squares  gave 

P=jS.  (43) 

Later,  Potter,*  to  protect  the  observer  from  the  lights  them- 
selves, substituted  a  translucent  screen  of  matt  glass,  or  paper, 
to  enable  the  observer  to  place  the  screen  between  himself  and 
the  lights. 

As  will  be  seen,  many  of  the  later  photometers  were  merely 
modifications  and  refinements  of  one  or  the  other  of  these 
primitive  forms. 

THE   RUMFORD,    OR   SHADOW   PHOTOMETER 

57.  This  apparatus  is  similar  to  that  designed  by  Bouguer, 
but  an  optical  device  replaces  the  partition.  The  method 
seems  to  have  been  first  devised  by  Lambert,  who,  in  1760, 
published  a  very  elaborate  study  of  illumination  and  its  com- 
parison.f  Subsequently  the  shadow  principle  was  employed  by 
Benjamin  Thompson  (Count  Rumford)  in  such  a  way  as  virtu- 
ally to  rediscover  its  use  to  scientists,  and  from  this  fact  it 
received  the  name  of  the  Kumford  Photometer.  £ 

Eumford  placed  a  white  screen  against  the  wall  and  held  a 
small  cylinder  of  wood  in  front  of  it,  about  two  or  three  inches 
in  length  and  one-quarter  of  an  inch  in  diameter.  The  lights 
were  then  moved  about  until  an  equality  of  the  shadows  was 

*  Edinburgh  Journal  of  Science,  New  Series,  III,  page  284. 

t  Photometria  sive  de  mensura  et  gradibus  luminis  colorum  et  umbrae, 
1760. 

J  Philosophical  Transactions,  1794,  Part  I,  page  67  ;  a  letter  to  Sir 
Joseph  Banks  from  Benjamin  Thompson  on  shadows,  etc. 


54 


PHOTOMETRICAL  MEASUREMENTS 


found,  when  their  relative  intensities  were  calculated  by  the 
law  of  inverse  squares. 

In  the  usual  form  of  the  apparatus  the  cylinder  was  perma- 
nently mounted  in  front  of  the  screen.  The  post  0  (Fig.  14) 
prevents  the  light  from  /S  from  falling  upon  the  screen  AB  at 
s,  and  similarly  the  light  from  P  at  p.  The  shadow  s  from  S 
will  be  illuminated  by  P,  and  in  turn  at  p  by  S.  These  two 


FIG.  14. 


separated  areas  are  thus  illuminated  by  the  lights  P  and  S 
severally,  and  when  they  are  brought  to  an  equality  of  illu- 
mination, 7-2 

P  =  jS,  (43  bis) 

the  distances  L  and  I  being  taken  from  the  lights  to  their 
respective  illuminations. 

The  two  light  vectors  PS  and  Sp  must  have  the  same  angle 
of  incidence  on  the  screen  AB,  otherwise  by  the  generalized 
photometrical  law,  T2  * 

p-yfH'  (44) 


PHOTOMETERS  55 

0  being  the  angle  made  between  Ps  and  AB ;  and  </>,  between 
Sp  and  AB. 

It  is  difficult  to  adjust  this  instrument  to  follow  the  require- 
ment of  equality  of  angles  of  incidence,  for  if  8  is  fixed  in  po- 
sition, P  must  be  moved  along  a  curved  path  from  0  as  the 
origin.  The  lack  of  sensitiveness  resulting  from  the  widely 
separated  areas  compared  does  not  justify  such  an  exact 
correction. 

The  screen  AB  may  be  translucent  and  viewed  from  the 
side  opposite  to  the  lights. 

THE   RITCHIE   PHOTOMETER* 

58.  A  radical  change  in  photometry  was  made  by  Ritchie 
leading  to  greater  compactness  of  apparatus  and  introducing 
the  possibility  of  greater  sensitiveness  in  the  results. 


Bitchie  placed  the  lights,  as  is  now  commonly  done,  in  fixed 
positions  at  the  end  of  a  bar,  viewing  the  illuminations  of  the 
screen  at  right  angles  to  the  common  line  of  the  lights,  and 
moving  the  screen  instead  of  the  lights  to  obtain  an  equality 
of  the  illuminations.  He  was  thus  enabled  to  enclose  his 
photometer  in  a  compact  sight  box. 

The  essential  feature  of  his  sight  box  t  were  two  mirrors,  Ml 
and  3/2,  Fig.  15,  placed  vertically  and  dihedrally  in  the  box,  and 
at  an  angle  of  45°  with  the  photometrical  axis.  That  the  reflect- 

*  For  a  recent  modification  of  this  screen,  see  an  account  of  the  Nichols- 
Ritchie  Screen,  Physical  Review,  1893,  page  339. 
t  Brewster's  Journal  of  Science  ;  5,  1826,  page  139. 


56  PHOTOMETRICAL  MEASUREMENTS 

ing  power  of  the  mirrors  might  be  more  nearly  equal  they  were 
cut  from  the  same  sheet  of  glass.  An  opening  in  front  of  the 
apex  of  the  mirrors  was  covered  with  a  translucent  screen  s.c. 
such  as  tissue  paper,  and  there  was  a  blackened  partition 
extending  from  the  edge  of  the  dihedral  angle  to  the  screen. 
The  box  was  reversed  at  each  setting  to  eliminate  inequalities. 
The  Ritchie  photometer  is  an  excellent  one,  and  can  be  given 
great  sensitiveness  by  substituting  prisms  for  the  mirrors  and 
employing  a  proper  diffusing  screen. 

He  also  discovered  the  properties  of  the  inclined  surface 
screen  and  used  this  form  in  his  investigations. 

THE   FOUCAULT  PHOTOMETER* 

59.  This  is  a  refinement  of  the  form  already  described  and 
attributed  to  Bouguer.  J.  Herschel  t  showed  that  the  wide 
separation  of  the  illuminated  areas  of  the  Lambert  photom- 
eter was  a  source  of  uncertainty  and  loss  of  sensitiveness,  and 
established  the  condition  that  maximum  sensitiveness  in  the 
comparison  of  two  illuminated  surfaces  required  them  to  be 
placed  immediately  side  by  side,  with  edges  sharply  defined 
and  divided  by  a  very  narrow  separating  line.  This  condition 
is  fairly  well  met  in  the  Foucault  photometer  by  removing  the 
partition  a  short  distance  from  the  screen  and  making  its 
position  adjustable  by  means  of  a  screw,  so  that  during  the 
observation  it  may  be  moved  until  its  shadow  is  reduced  to  a 
narrow  band.  This  line  of  separation,  however,  is  not  perfectly 
dark  and  distinct,  for  it  is  partially  lighted  by  irradiation  from 
both  light  sources,  which  also  causes  the  edges  of  the  illumi- 
nated areas  to  lose  their  sharpness. 

In  order  to  reduce  this  disturbance  a  double  screen  was  used 
with  its  sides  inclined  from  the  observer,  forming  an  obtuse 
angle,  the  dividing  shadow  being  received  at  its  apex  (Fig. 
16).  The  two  lights  P  and  S  were  ranged  respectively  along 

*  CEuvres  Completes,  page  100. 
t  On  Light,  page  29. 


PHOTOMETERS  57 

the  normal  to  each  surface  Al  and  A2,  and  both  the  adjustment 
of  their  positions  and  the  calculation  of  their  relative  intensities 
follow  methods  already  described.  The  Lambert  translucent 
screen  was  used  in  this  apparatus,  and  this,  together  with  the 


FIG.  16. 

movable  partition,  were  mounted  in  a  containing  sight  box 
fitted  with  a  hood  to  protect  the  eyes  from  the  compared 
lights. 

THE   WEDGE-SHAPED  SCREEN 

60.  After  placing  the  reflecting  mirrors  in  a  sight  box, 
movable  along  the  axis  of  the  compared  lights,  Ritchie*  pro- 
ceeded to  simplify  the  photometer,  and  combined  the  diffusion 
and  reflection  of  the  light  on  one  surface  by  substituting  sheets 
of  paper  for  the  reflecting  mirrors. 

He  mounted  pieces  of  cardboard,  cut  from  the  same  sheet, 
and  placed  with  like  surfaces  outward  in  the  place  of  the 
mirrors,  Figure  15.  A  wedge-shaped  screen  was  the  result, 
which  was  viewed  from  the  opening  in  the  sight  box  from 
which  the  tissue  paper  screen  and  the  partition  used  with  the 
reflecting  mirrors  were  removed. 

*  Ritchie,  reference  cited. 


58  PHOTOMETRICAL   MEASUREMENTS 

61.  On  the  theory  of  the  wedge-shaped  screen.  — The  sides  of 
the  wedge  screen  must  be  symmetrically  placed  in  the  photo- 
metrical  axis,  that  the  light  may  be  incident  at  the  same  angle 
upon  each  surface.     For  if  ft  and  ft  be  the  normal  illumi- 
nations on  the  screen  faces  respectively,  and  Q\  and  Q'3  the 
reflected  light,  and  «j  and  a2  the  coefficients  of  reflection,  and 
6  and  <£  the  angles  of  inclination  of  the  sides  to  the  photomet- 

rical  axis,  then 

Q'i  =  aiQiCos(9,  (45) 

and  Q'2  =  a2Q2  cos  <£,  (46) 

or  ft  ,0,0'!  cos  ^.  (47) 

Q2     a,Q'2  cos  e 

The  photometrical  law  requires  that  ft  and  ft  shall  be  equal 
for  the  condition  of  the  photometrical  balance,  and  certainty 
in  the  working  of  such  a  screen  equally  requires  that  Q\  and 
Q'2  shall  be  equal. 

These  requirements  are  met  by  placing  the  sides  of  the  screen 
at  the  same  angle  toward  the  photometrical  axis  and  using  sur- 
faces of  like  reflecting  power  on  each  side  of  the  wedge.  The 
most  efficient  reflecting  angle  will  be  discussed  in  a  subsequent 
paragraph. 

62.  The  Conroy  photometer.  —  Within  recent  years  the  wedge 
screen  has  again  received  attention.      Experimenting  with  a 
Ritchie  wedge,  Conroy  *  experienced  much  difficulty  with  the 
apex  of  the  wedge.     If  the  paper  was  bent  around  this,  there 
was  no  well-marked  line  of  separation  between  the  two  sides ; 
nor  by  cutting  the  paper  and  matching  the  edges  was  the  sepa- 
ration as  sharp  as  he  desired.    For  maximum  sensitiveness  the 
two  illuminated  fields  should  meet  in  a  common  dividing  line, 
which  should  be  entirely  distinct  and  very  narrow. 

He  secured  high  sensitiveness  by  modifying  the  Eitchie 
wedge.  In  the  sight  box  shown  in  plan  in  Figure  17,  A±  and 

*  Philosophical  Magazine  ;  15,  1883,  page  423. 


PHOTOMETERS 


59 


A2  are  two  wooden  prisms  fastened  to  the  base,  placed  so  that 
the  sides  Bl  and  B2  make  an  angle  of  60°  with  the  photonic  t- 
rical  axis  xx'.  Similar  pieces  of  white  paper  or  cardboard 
were  attached  to  them,  and  the  piece  mounted  at  B2  nad  the 
edge  toward  the  second  prism  trimmed  sharp  and  straight. 


FIG.  17. 

The  halves  of  the  screen  were  illuminated  through  the  open- 
ings Ci  and  C2  respectively,  and  the  prisms  were  staggered  on 
the  base  so  that  the  eye  placed  at  the  opening  E  would  see  the 
side  B2  projected  on  J5lt  This  form  has  the  disadvantage  that 
one  half  the  screen  is  nearer  the  eye  than  the  other. 

Conroy  also  studied  the  best  angle  of  reflection.     He  found 
that  when  light  was  incident  on  the  paper  surface  at  an  angle 


60 


PHOTOMETRICAL  MEASUREMENTS 


of  45°,  considerable  glare  or  specular  reflection  occurred.  This 
was  completely  obviated  by  reducing  the  incident  angle  to  30°; 
which  would  indicate  that  for  the  simple  reflecting  wedge  of 
Ritchie,  the  dihedral  angle  should  be  60°. 

63.  The  Thompson  photometer. — The  Ritchie  wedge-shaped 
screen  was  revived  some  years  since,  and,  though  practically 
unmodified.  ™as  known  commercially  as  the  Thompson-Starling 
screen.  These  experimenters  experienced  a  like  difficulty  with 
the  lack  of  sharpness  of  definition  of  the  apical  edge  of  the 
screen.  They  also  found  that  a  dihedral  angle  of  90°  gave 
considerable  specular  reflection  that  interfered  with  the  work- 
ing of  the  screen,  so  they  finally  adopted  a  working  angle  of 
70°.  The  material  of  the  screen  was  cardboard,  and  they 
endeavoured  to  compare  lights  of  different  colours  by  using  a 
surface  corresponding  in  tint  to  the  light,  a  plan  which  fails  to 
yield  the  desired  result,  and  which  may  introduce  an  error 
through  the  unlikeness  of  the  screen  surfaces. 

Subsequently  Thompson*  devised  a  modified  screen,  which 
is  really  an  inverted  Ritchie  wedge.  The  reflecting  faces  of  a 


FIG.  18. 


wooden  prism  were  covered  with  cardboard,  as  in  other  cases ; 
but  this  was  so  cut  at  the  edges  that  tongues  projected  at  each 
side,  as  is  shown  in  Figure  18  in  plan  and  elevation.  The 

*S.  P.  Thompson,  Philosophical  Magazine;  36,  1893,  page  120. 


PHOTOMETERS  61 

tongue  B  is  illuminated  by  one  light  source,  and  the  tongues 
AI  and  A2  by  the  other.  The  impression  on  the  eye  made  by 
the  illumination  of  the  tongue  is  supported  by  the  similar 
illumination  of  the  card  surface  from  which  the  tongue  pro- 
jects. At  the  same  time,  after  the  manner  of  the  Conroy 
screen,  of  which  this  is  a  development,  the  illumination  of 
one  field  is  projected  on  that  of  the  other. 

This  form  of  screen  has  much  to  commend  it.  The  remain- 
ing details  of  the  photometer  were  similar  to  those  used  by 
Eitchie. 

THE   PAKAFFINE   DIFFUSION   SCREEN 

64.  This  form  of  screen  suggested  by  Elster  *  may  consist 
of  a  two-inch  cube  of  homogeneous  paraffine  which  is  divided 
centrally,  and  a  thin  sheet  of  metal  or  other  substance  imper- 
vious to  light  and  not  attacked  by  the  impurities  in  the  paraf- 
fine is  inserted  between  the  halves  and  the  whole  then  pressed 
firmly  together.  The  cube  is  placed  in  the  usual  form  of  sight 
box  and  centred  in  the  photometrical  axis,  with  the  dividing 
plane  at  right  angles  to  it. 

The  light  falling  normally  on  the  faces  of  the  cube  is 
spherically  diffused,  and  each  half  of  the  cube  being  illumi- 
nated from  its  respective  light  source,  will  present  two 
illuminated  fields  from  the  face  toward  the  observer.  The 
fields  will  be  sharply  defined  from  each  other  by  the  thin 
partition,  and  an  easily  read  and  fairly  sensitive  screen  is  the 
result.  The  diminution  of  the  light  is  the  marked  disadvan- 
tage of  this  form  of  screen.  Instead  of  paraffine,  any  trans- 
lucent solid,  such  as  stearine,  may  be  employed. 

A  permanent  screen  may  be  made  from  plates  of  opal  glass, 
but  this  material  is  objectionable  in  that  it  alters  the  quality 
of  the  light  by  differential  or  selective  reflection. 

This  type  of  screen  may  be  given  almost  any  degree  of 
sensitiveness  that  an  investigator  may  desire,  by  constructing 
an  optical  cube  with  plate  glass  faces  and  placing  in  it  a  thin 
*  Carl  Reportorium,  IV,  1868,  page  171. 


62  PHOTOMETRIC AL  MEASUREMENTS 

metal  partition,  which,  however,  should  not  extend  entirely  to 
the  back  of  the  cube. 

This  vessel  is  filled  with  distilled  water,  and  a  few  drops  of 
stannous  chloride  are  added,  and  the  liquid  stirred,  until  it  is 
uniformly  diffused.  By  decomposition,  basic  stannous  chloride 
is  formed,  and  imparts  a  milkiness  to  the  liquid.  The  precip- 
itate is  very  finely  divided,  and  if  dense  may  act  in  the  same 
injurious  manner  on  the  quality  of  the  light  as  opal  glass. 

THE   BUNSEN  PHOTOMETER 

65.  This  is  one  of  the  oldest  forms,  dating  from  1841, 
and  still  remains  the  most  widely  used  and  generally  efficient 
means  for  comparing  the  intensity  of  luminous  sources. 


L 

i\< 

II 

W 

II 

\! 

0-\ 

V1 

°\ 

1                             2                            3                           i    \ 

FIG.  19. 

Its  marked  simplicity  admirably  adapts  it  for  use  both  in 
the  laboratory  and  in  general  practice.  The  type  is  shown  in 
Figure  19. 

In  its  simplest  form,  a  sheet  of  white  paper  whose  centre 
has  been  rendered  transparent  with  paraffine,  stearine,  or  other 
suitable  material,  is  stretched  on  a  frame.  The  transparent 
portion  is  given  the  shape  of  a  circle  or  other  geometrical 
figure,  and  it  is  essential  that  the  edges  of  the  design  should 
be  sharply  defined.  The  screen  is  usually  mounted  in  a  sight 
box  which  is  movable  in  the  photometer  axis,  the  arrangement 
being  that  of  the  Ritchie  photometer. 

66.  The  action  of  the  Bunsen  screen. — The  screen  is  so  placed 
on  the  photometer  bench  that  the  axis  will  pass  through  the 
centre  of  the  transparent  spot.  The  light  falling  on  either 


PHOTOMETERS  63 

side  is  in  part  reflected  from  the  white  paper  surface  as  in  the 
case  of  similar  screens ;  and  a  portion  passes  through  the 
transparent  spot,  while  a  small  amount  of  light  is  lost  by 
absorption  in  each  portion  of  the  screen. 

The  coefficient  of  reflection  of  the  untreated  portion  of  the 
paper  is  much  greater  than  that  of  the  transparent  portion; 
then  so  far  as  the  action  of  the  light  facing  the  side  of  the 
screen  under  observation  is  concerned,  it  will  be  reflected  more 
strongly  from  one  portion  than  the  other,  and  the  transparent 
spot  will  appear  somewhat  dark  on  a  white  background. 
Assuming  the  light  on  the  opposite  side  to  be  of  the  same  tint, 
a  certain  amount  will  be  diffused  in  the  transparent  portion 
and  be  transmitted  through  it.  Neglecting  the  absorption  in 
the  screen  itself,  when  an  equal  quantity  of  light  is  trans- 
mitted in  each  direction,  the  illumination  of  the  spot  should 
appear  equally  bright  with  that  on  the  remainder  of  the  screen, 
and  the  spot  may  no  longer  be  distinctly  visible.  Then,  were 
both  sides  of  the  screen  identical,  and  there  was  no  marked 
absorption  of  light  in  the  transparent  spot,  this  would  be  no 
more  visible  on  one  side  than  the  other;  and  with  some  suit- 
able optical  arrangement  for  viewing  both  sides  simultaneously 
they  should  appear  equally  illuminated. 

The  distance  from  the  paper  to  the  respective  light  sources 
may  then  be  taken  and  the  relative  intensity  of  the  compared 
source  calculated  in  the  usual  manner. 

67.  The  mirrors. — In  order  to  present  the  two  sides  of  the 
screen  simultaneously  to  the  eye,  two  small  mirrors,  ra  and  m', 
Figure  20,  are  used.  These  are  placed  vertically  and  form  a 
dihedral  angle  with  each  other  of  120°  to  140°,  the  precise 
angle  being  determined  by  the  arrangement  of  the  sight  box. 
Practically  the  mirrors  may  be  adjusted  without  direct  refer- 
ence to  the  magnitude  of  the  dihedral  angle,  though  it  is 
essential  that  each  mirror  make  the  same  angle  with  the  sur- 
face of  the  paper. 

This  arrangement  is  frequently  called  the  Budorff  mirrors ; 


64 


PHOTOMETRICAL   MEASUREMENTS 


but  this  is  an  error  in  nomenclature,  since  it  is  not  known  who 
first  suggested  it.  * 

It  is  essential  that  the  mirrors  be  as  nearly  alike  in  reflect- 
ing power  as  possible,  or  the  unequally  illuminated  fields  will 
cause  confusion,  unless  the  attention  is  wholly  given  to  the 
comparison  of  the  illumination  of  the  spot  with  the  balance  of 


FIG.  20. 

the  screen.  Though  by  means  of  mirrors  both  fields  are  simul- 
taneously presented  to  the  eye,  they  appear  separated  by  a 
considerable  distance,  a  condition  which  has  been  shown  to 
reduce  the  sensitiveness  of  the  setting.  Yet,  from  one  stand- 
point, this  condition  may  be  made  an  unessential  in  the  use  of 
the  Bunsen  screen.  If  advantage  is  to  be  taken  of  the  com- 
pound character  of  the  screen,  then  the  comparison  is  between 

*  Riidorff  himself  speaks  of  using  the  known  method  of  two  mirrors 
about  120°  apart ;  Schilling's  Journal,  1869,  page  283.  Bohn  states  that 
"  mirror  photometers  have  long  been  in  use  without  it  being  known  who 
originated  the  device."  Annalen  der  Chemie  und  Pharmacie,  1859,  VoL 
III,  page  335. 


PHOTOMETERS  65 

the  illuminated  surfaces  of  the  transparent  spot  and  the  cir- 
cumjacent area,  and  with  a  screen  of  like  surface  on  each  side, 
no  comparison  need  be  instituted  between  the  two  fields  except 
in  the  special  case  to  be  discussed  later. 

Should,  however,  a  comparison  be  desired  between  the 
intensity  of  illumination  of  each  side,  the  two  fields  must 
be  presented  to  the  eye,  lying  in  contact,  and  separated  by 
a  very  narrow  line.  Optical  devices  for  accomplishing  this 
have  been  designed  both  by  Von  Hefner- Alteneck  and  Kriiss.* 
(See  page  71.) 

68.  The  preparation  of  the  Bunsen  screen.  —  The  occasion  fre- 
quently arises  with  the  photometrician  to  prepare  such 
screens,  for  they  soil  readily  and  deteriorate  after  a  time.  It 
is  somewhat  difficult  to  select  a  suitable  quality  of  paper.  For 
the  ordinary  type  of  screen  the  paper  should  be  of  fine  yet 
firm  texture ;  it  should  be  of  medium  thickness,  without  being 
especially  translucent ;  and  the  surface  should  be  smooth, 
though  neither  glazed  nor  highly  calendered.  A  medium 
weight,  white,  and  smooth  linen  bond  or  ledger  paper  will 
make  very  good  screens. 

The  transparent  spot,  as  has  been  suggested,  must  be  per- 
fectly sharp  in  outline  for  satisfactory  sensitiveness  in  the 
setting.  A  greased  spot  will  obviously  not  meet  these  require- 
ments. Paraffine  and  stearine  are  suitable  materials  for 
making  the  transparent  spot,  and  the  material  should  be  heated 
and  printed  upon  the  paper. 

A  method  successfully  used  by  the  author  f  consists  in 
cutting  a  design,  such  as  a  star  or  a  circle,  about  one  inch 
in  diameter,  from  sheet  brass;  this  is  then  fastened  to  a 
handle  (Fig.  21).  The  plate  is  heated  until  parafnne  or 
stearine  placed  upon  it  melts  and  runs  freely.  The  excess  is 
allowed  to  drain  off,  and  when  the  material  is  on  the  point  of 
solidifying,  the  design  is  firmly  pressed  on  the  sheet  of  paper. 

*  Schilling's  Journal,  1884,  page  587. 

t  W.  M.  S.,  Electrical  Industries,  January,  1896,  page  7. 

F 


66  PHOTOMETRICAL   MEASUREMENTS 

A  piece  of  clean  white  blotting  paper  is  then  laid  over  the 
screen  and  pressed  with  a  hot  iron,  in  order  to  drive  the  print 
into  the  texture  of  the  paper.  If  due  care  is  exercised  in  the 
details,  very  sharply  outlined  prints  can  be  made. 


j 


FIG.  21. 

69.  The  theory  of  the  Bunsen  screen.  —  Though  the  screen 
itself  is  exceedingly  simple  in  construction,  the  theoretical 
considerations  involved  in  its  action  are  by  no  means  so ;  yet 
the  elements  of  its  theory  are  essential  to  the  merest  practician 
in  order  to  avoid  its  erroneous  use. 

The  light  incident  upon  each  side  of  the  screen  is  partially 
reflected,  transmitted,  and  absorbed  by  it.  Recalling  that 
the  untreated  portion  of  the  paper  is  also  translucent,  its 
action  is  seen  to  be  similar  to  that  of  the  transparent  spot, 
though  the  components  in  its  action  differ  in  degree  from 
the  others. 

The  symbols  with  their  definitions,  which  will  be  employed, 
are: 

r,   the  coefficient  of  reflection. 

t,    the  coefficient  of  transmission. 

a,   the  coefficient  of  absorption  in  the  screen. 

L,  the  intensity  of  the  incident  illumination. 

S,  the  intensity  of  illumination  emitted  by  the  screen. 

dy   the  distance  between  the  screen  and  the  light  source. 

d)  etc.,  parts  on  the  left  of  the  screen. 

(2)  etc.,  parts  on  the  right  of  the  screen. 

(')  refers  to  the  transparent  spot. 

Quantities  unaccented  refer  to  the  untreated  portion  of  the 
screen. 


PHOTOMETERS  67 

The  general  formulas  for  a  screen,  reflecting,  transmitting, 
and  absorbing  the  incident  light,  are : 


(48) 

+  a      =1,) 

an  axiomatic  statement  first  proposed  by  Lambert.* 

The  luminous  intensity  of  the  screen  S  will  be  less  than  the 
intensity  of  the  incident  light  L  by  an  amount  due  to  ab- 
sorption within  the  screen,  thus  : 

S  =  (r  +  t)  L  =  L  (1  —  a).  (49) 

For  the  present,  then,  only  reflected  and  transmitted  light 
will  be  discussed.  Proceeding  from  the  general  statement  of 
equation  49,  the  visual  action  of  the  screen  may  be  expressed 
by  four  equations : 

Untreated  paper,  left  side, 

51  =  LiTi  -f-  LJ.  (50) 
Transparent  spot,  left  side, 

Si1  =  LiTi'  +  Lf-  (51) 

Untreated  paper,  right  side, 

52  =  L2r2  +  Lit.  (52) 
Transparent  spot,  right  side, 

S9'  =  L2r2'  +  LJ.  (53) 

And  L  may  be  specified  from  the  general  expression, 


=      , 

a2 

where  A:  is  a  constant  connecting  the  luminous  intensity  /  of 
the  light  source  with  the  amount  of  light  from  it  falling  on 
unit  surface  at  unit  distance  in  terms  of  the  unit  taken  for  d, 

(page  31). 

*  J.  H.  Lambert,  Photometria,  1760. 


68  PHOTOMETRIC AL   MEASUREMENTS 

From  the  four  equations  (50-53)  certain  conditions  may  be 
deduced.  The  first  adjustments  suggested  are: 

(1)  That  which  will  make  Si  =  Si,  when  the  spot  should 
practically  disappear  on  the  left  and  the  entire  surface  of  the 
screen  appear  to  be  equally  illuminated. 

(2)  That  which  will  make  S2  —  S2,  when  the  spot  should 
similarly  disappear  on  the  right  side. 

In  practice  it  will  be  found  that  Si  =  $/  and  S2  =  S2'  are 
each  smaller  than  a  true  mean  value  /S",  which  would  represent 
the  intensity  of  the  illumination  were  /Sj  =  S%  and  but  one 
setting  of  the  screen  needed;  the  amount  of  the  decrement 
depends  entirely  on  the  nature  of  the  screen.  This  suggests  a 
third  possible  adjustment. 

9         ^ 

(3)  That  which  will  make  -^  =  -—„  or  there  will  be  an  equal 

Oj  O£ 

contrast  between  the  untreated  screen  and  the  spot  on  each 
side,  and  the  screen  will  then  be  at  a  true  mean  setting. 

70.  The  practice  with  the  screen  may  follow  one  of  three 
cases : 

I.  Either  side  of  the  screen  may  be  used  singly,  neglecting 
the  other.     One  setting  is  made  facing  the  left  and  a  balance 
obtained  with  Si  =  Si  ;  the  screen  is  then  reversed  and  a  simi- 
lar setting  yields  S2  =  Sa'.     The  mean  of  the  two  settings  is 
taken  for  calculating  the  intensity  of  the  compared  lights. 

This  method  is  advised  only  in  case  the  light  sources  are  of 
similar  tint,  and  the  spot  can  be  made  to  disappear.  The 
mean  value  for  the  setting  is  slightly  in  error  when  the  screen 
is  placed  at  a  considerable  distance  from  the  centre  of  the  bar, 
though  the  error  may  be  considered  as  negligible  in  ordinary 
practice. 

II.  Four  settings   may  be   made,  using  both   sides  of  the 
screen.     The   adjustment  Si  =  Si    is   made   to   the   left   and 
S2  =  S2  to  the  right.    To  obviate  an  error  due  to  the  inequality 
of  the  sides,  the  screen  and  mirrors  as  well  are  reversed  and 
two  similar  settings  are  made.     The  mean  of  the  four  settings 


PHOTOMETERS  69 

is  then  taken.  The  restrictions  regarding  the  colour  of  the  lights 
apply  equally  in  this  method.  It  offers  no  advantages  over  the 
first  method,  and  requires  four  instead  of  two  settings. 

III.   The  screen  is  adjusted  for  equal  contrasts  on  each  side 

or  o 

with  -^  =  —2  ;  and  the  screen  and  mirrors   being  reversed,  a 
8i<     S2 

similar  setting  is  made,  and  the  mean  of  the  two  taken.  This 
method  is  recommended  for  general  practice,  as  it  will  enable 
lights  which  differ  in  colour  to  be  compared. 

71.  The  sensitiveness  of  the  Bunsen  screen  may  be  examined 
in  a  general  way.  If  a  screen  of  this  character  should  be  so 
placed  that  LI  =  L2,  then  from  equation  49 


a  relation  which  would  hold  true  only  in  one  case,  that  the 
lights  suffered  equal  absorption  in  their  passage  through  each 
portion  of  the  screen.  When  the  screen  is  made  from  a  single 
sheet  of  paper,  then  a>a';  and  it  follows,  even  should  both 
sides  of  the  screen  be  identical,  that  at  no  one  setting  will 
the  condition  be  simultaneously  obeyed,  Si  =  Si'  =,Sa  =  S2'. 
Greater  sensitiveness  follows  increased  transparency  in  the 
spot,  providing  it  still  diffuses  the  light  sufficiently;  but  at  the 
same  time,  a'  also  decreases. 

The  ideally  sensitive  screen  would  be  one  having  zero  values 
for  a,  a',  and  £;  while  the  value  of  t1  approached  unity,  and 
that  of  r',  zero. 

The  increase  of  the  transparency  of  the  spot  must  be 
governed  by  the  requirements  for  complete  diffusion  of  the 
light  transmitted;  otherwise,  the  illumination  from  the  spot 
can  not  be  properly  compared  with  that  from  the  remainder  of 
the  screen. 

Various  modifications  of  the  Bunsen  screen  are  possible.  An 
opaque  instead  of  a  transparent  spot  may  be  formed  on  a  sheet 
of  translucent  paper  ;  or  a  thin  sheet  of  opaque  material  may 
be  inserted  between  two  sheets  of  paper  to  prevent  the  passage 


70  PHOTOMETRIC AL  MEASUREMENTS 

of  light  from  one  side  to  the  other  through  the  untreated  por- 
tion, an  opening  being  made  in  it  for  the  transparent  spot. 
The  more  nearly  alike  the  surface  and  texture  of  both  parts 
of  the  screen  are  made,  the  more  readily  the  transparent  spot 
will  disappear. 

The  sensitiveness  of  any  modification  of  the  Bunsen  screen 
may  be  studied  from  the  equations  given  above.* 

THE  LUMMER-BRODHUN  PHOTOMETER 

72.  This  optical  train  is  otherwise  known  as  the  Reichsanstalt 
photometer,  having  been  developed  in  connection  with  photo- 
metrical  investigations  carried  out  under  its  auspices.f  Its 
essential  feature  is  also  named  an  optical  screen,  a  term  mani- 
festly incorrect  to  distinguish  this  photometrical  device  from 
other  screens  with  their  accessories.  This  name  originated 
in  the  announcement  of  the  designers  of  their  "substitution 
of  a  purely  optical  combination  for  the  photometrical  grease 
spot."  J 

A  diffusing  screen,  ik  (Fig.  24),  whose  coefficient  of  absorp- 
tion is  as  low  as  possible,  is  centred  normally  to  the  photo- 
metrical  axis,  following  in  a  sense  the  Ritchie  arrangement. 
The  characteristic  feature  of  this  photometer  is  the  optical 
device  for  simultaneously  viewing  both  sides  of  the  screen, 

*  The  theory  of  the  Bunsen  screen  was  early  developed  by  Bohn, 
Annalen  der  Chemie  und  Pharmacie,  1859,  page  335;  and  later  by 
Riidorff,  Schilling's  Journal,  1869,  page  285.  Probably  the  best  dis- 
cussion is  given  by  Leonhard  Weber,  Annalen  der  Physik  und  Chemie, 
31, 1887,  page  676.  Discussions  by  Liebenthal  may  be  found  in  Schilling's 
Journal,  1889,  pages  76  and  116 ;  and  in  the  Elektrotech.  Zeitschrift,  1888, 
page  102. 

t  It  appears  that  the  Lummer-Brodhun  optical  screen  was  anticipated 
by  Professor  William  Swan  of  the  University  of  St.  Andrews.  His 
apparatus  is  described  in  the  Transactions  of  the  Royal  Society  of  Edin- 
burgh, Vol.  16,  1849,  and  Vol.  22,  1859  ;  also  consult  Philosophical  Maga- 
zine, January,  1900,  page  118. 

J  O.  Lummer  and  E.  Brodhun,  Zeitschrift  fur  Instrumentenkunde,  1889, 
pages  23  and  41. 


PHOTOMETERS 


71 


presenting  to  the  eye  light  reflected  from  them  as  adjacent  fields 
of  vision.  Krtiss  had  accomplished  this  in  1884  *  in  a  manner 
closely  analogous  to  that  under  discussion  (see  Fig.  22) . 


73.  The  action  of  the  optical  train,  t  — The  diffused  light 
reflected  from  the  sides  of  the  screen  Zx  and  12  falls  on  the 
mirrors  /x  and  /2,  and  thence  is  reflected  along  the  normal  to  the 
surfaces  of  the  triangular  prisms  A  and  B.  The  observer  look- 
ing through  the  telescopic  sight  tube  ow  directed  normally  to  ac 
clearly  views  the  interior  surface  arsb  of  the  prism  B.  The 
light  from  /2  will  be  totally  reflected  to  ow  from  the  portions 
of  the  surface  sb  and  ar,  while  that  falling  on  rs  will  be  trans- 
mitted through  A,  and  will  not  appear  in  the  fields  to  be  com- 
pared. That  portion  of  the  light  from  f±  which  falls  on  rs  will 

*  Schilling's  Journal,  1884,  page  587. 

t  Schilling's  Journal,  1892,  No.  29,  page  573. 


72 


PHOTOMETRICAL   MEASUREMENTS 


be  transmitted  through  B  to  ow,  while  the  light  falling  on  the 
portions  gr  and  ps  will  be  likewise  reflected  out  of  the  field 
of  vision.  The  observer  will  then  view  a  three-part  field ;  the 
central  band  being  diffused  light  from  /1?  and  the  other  portions 
from  .& 

This  optical  train  is  mounted  in  a  compact  sight  box  (Fig. 
23),  carefully  blackened  on  its  interior  to  absorb  the  dispersed 
light. 


FIG.  23. 

74.  The  adjustment  of  the  optical  train.  —  Great  care  and 
precision  are  required  in  the  adjustment  of  the  component 
parts,  and  when  this  is  properly  done,  the  conditions  are 
met,  that: 

1.  The  plane  of  the  contact  surfaces  at  rs  (Figs.  24  and  25) 
must  coincide  with  the  plane  of  the  screen  ik  [or  c'd]  ;  or,  both 
these  surfaces  and  the  central  plane  of  the  screen  must  lie  in 
the  vertical  plane  through  the  axis  of  the  box.  If  this  latter 
be  taken  as  the  plane  of  symmetry,  then,  Figure  25, 


PHOTOMETERS 


73 


2.   The  reversing  axis  uz  of  the  box  lies  in  the  plane  of  sym- 
metry; and 

i 


B   >e 


FIG.  24. 


3.   It  passes  through  the  centres  of  the  contact  surfaces  rs 
and  the  screen  ik  (Fig.  24). 


FIG.  25. 


74  MOTOMETRICAL  MEASUREMENTS 

4.  The  edges  of  the  prisms  A  and  B  must  be  perpendicular 
to  the  reversing  axis  and  parallel  with  the  plane  of  symmetry, 
while 

5.  The  mirrors  /L  and  /2  must  also  be  parallel  with  the  plane 
of  symmetry,  so  that 

6.  The  centres  of  the  two  mirrors,  the  surface  rs,  and  the 
screen  ik  shall  lie  in  a  common  plane,  itself  perpendicular  to 
the  plane  of  symmetry;    and  the  lines  joining  these  centres 
should  form  a  square.     This  common  plane  for  the  centres  con- 
stitutes the  principal  horizontal  section  through  the  box ;  and 
contains,  besides  the  axis  of  reversal  uz  of  the  box, 

7.  The  axis  of  the  sight  tube  ow,  which  also  must  be  perpen- 
dicular to  the  surface  ac  of  the  prism  B,  Figure  24. 

The  principal  mechanical  provisions  for  readily  and  surely 
accomplishing  these  requirements  are  clearly  outlined  in  Fig.  25. 

When  properly  adjusted,  the  operator  looking  through  the 
sight  tube  views  two  illuminated  fields  side  by  side,  and  is 
enabled  to  obtain  the  photometrical  balance  in  the  usual  manner. 

The  distance  from  the  screen  to  the  lights  is  measured  be- 
tween them  and  the  face  of  the  screen.  The  screen  is  made  by 
filling  in  an  opening  in  a  brass  plate,  about  three  millimetres 
in  thickness,  with  calcium  sulphate  or  magnesium  oxide.  The 
screen  being  so  thick,  an  error  will  be  introduced  in  consequence 
if  measurements  are  taken  from  the  position  of  the  pointer 
attached  to  the  sight  box.  To  allow  for  this,  the  distance 
between  the  two  light,  sources  as  read  should  be  corrected  by 
the  amount  of  the  thickness  of  the  screen. 

75,  The  composite  sight  field.  —  The  sight  field  in  the  improved 
apparatus  is  usually  divided  into  four  contrasting  portions,  by 
an  ingenious  application  of  the  principle  of  the  total  reflection 
of  light.  These  divisions  are  given  the  outline  shown  in  Figure 
26  or  27. 

The  process  consists  in  cutting  out  stencils  from  thin  sheet 
copper  having  the  shape  of  the  portions  ^  and  12,  Figure  27. 
These  are  cemented  on  the  hypothenusal  face  of  the  prism 


PHOTOMETERS 


75 


A,  and  the  unprotected  portion  is  cut  away  with  a  sand  blast 
to  a  slight  depth.  The  hypothenusal  faces  of  the  prisms  A 
and  B  have  previously  been  ground  and  polished  on  each 


FIG.  26. 


other  to  insure  perfect  contact ;  and  after  the  etching  is  com- 
pleted they  are  firmly  clasped  together,  and  pressure  is  applied 
until  their  entire  polished  surfaces  are  in  contact,  and  are  com- 
pletely transparent. 


FIG.  27. 

The  light  from/2,  normally  incident  on  the  face  be  is  now 
totally  reflected  from  r-±  and  r2,  because  the  film  of  air  back  of 
them  introduces  a  rarer  medium  in  contact  with  the  denser 
glass,  resulting  in  total  reflection  of  the  light  at  these  points 
which  thence  passes  out  normally  to  ac  into  the  sight  tube. 


76  PHOTOMETRICAL  MEASUREMENTS 

That  portion  of  the  light,  however,  which  falls  on  the  faces  ^ 
and  12,  which  are  perfectly  transparent,  passes  through  and 
emerges  from  the  face  ad  and  is  absorbed  by  the  black  coating 
on  the  interior  of  the  sight  box.  Similarly,  the  light  normally 
incident  on  bd  is  both  totally  reflected  from  rx  and  rs  and  ab- 
sorbed by  the  coating  on  the  box ;  and  is  transmitted  through  ^ 
and  12  to  the  sight  tube.  The  rays  of  light  from  both/!  and/2 
pass  through  the  same  thickness  of  glass  in  reaching  the  sight 
tube  and  thus  suffer  equal  diminution  by  its  absorption,  pro- 
viding the  glass  is  homogeneous  in  both  prisms.  This  ingenious 
sight  field  is  one  of  the  most  elegant  applications  of  the  prin- 
ciples of  optics  to  photometry. 

76,  The  contrast  principle.* —  The  eye  rapidly  grows  fatigued 
when  viewing  an  equally  illuminated  surface,  and  its  sensi- 
tiveness at  best  is  low  for  slight  differences  in  intensity. 
In  an  endeavour  to  obviate  such  disadvantage,  the  designers 
have  introduced  into  this  optical  train  a  certain  device  which 
produces  a  well-marked  contrast.  This  is  considered  espe- 
cially valuable  when  comparing  lights  which  differ  somewhat 
in  colour. 

The  contrast  is  accomplished  by  darkening  the  portion  of 
the  field  r:  and  l^  by  interposing  a  thin  glass  absorbing  strip 
in  the  path  of  the  active  light.  The  strip  gb  is  placed  in  front 
of  the  face  of  the  prism  A,  covering  this  to  such  an  extent  that 
the  light  transmitted  through  the  face  ^  from  flt  Figure  27, 
is  decreased  in  intensity.  The  strip  me  is  similarly  placed 
over  the  face  of  the  prism  B  and  darkens  the  light  totally  re- 
flected from/2. 

Should  the  comparison  lights  have  the  same  colour,  when  a 
balance  is  obtained  the  symmetrical  portions  of  the  field  will 
have  the  same  intensity  of  illumination,  while  between  these 
there  will  be  a  marked  difference  in  intensity  amounting  to 
about  8  per  cent,  which  rests  the  eye,  and  enables  it  to  be 
worked  at  its  maximum  sensitiveness. 

*Zeitschrift  fur  Instruinentenkunde,  1889,  page  461. 


PHOTOMETERS  77 

77.  Working  directions.  —  When  the  lights  to  be  compared 
are  of  the  same  colour,  and  the  train  is  used  without  the  absorb- 
ing strips,  adjust  the  telescopic  sight  tube  until  the  different 
portions  of  the  field  are  sharply  outlined,  the  sight  box  being 
moved  to  a  position  showing  considerable  contrast.     The  sight 
box  is  then  moved  to  a  position  in  which  the  outlines  of  the 
field  disappear,  and  there  results  a  practically  uniformly  illumi- 
nated area.      This  adjustment  is  then  tested  by  moving  the 
sight  box  slightly  both  to  the  right  and  the  left,  until  a  distinct 
contrast  is  visible  in  each  case.     The  box  is  finally  brought 
back  to  the  position  of  a  balanced  field.     The  setting  having 
been  noted,  the  box  is  reversed  on  its  axis,  to  avoid  error  aris- 
ing from  inequality  of  the  mirrors  or  screen,  and  the  mean  of 
the  two  positions  is  taken.     Differently  coloured  lights  can  not 
be  compared  in  this  manner. 

Or,  insert  the  absorbing  strips,  and  adjust  the  position  of  the 
sight  box  until  a  similar  contrast  is  found  between  the  central 
portions  and  the  adjacent  parts ;  that  is,  between  r^  and  12,  and 
?*2  and  /!.  The  dividing  line  between  the  adjoining  portions 
12,  and  r2,  will  not  wholly  disappear  except  with  lights  of 
identical  colour.  Since  in  the  balanced  position  there  is 
already  a  distinct  contrast,  the  setting  need  not  be  proven  by 
lateral  movement  of  the  sight  box  as  in  the  preceding  case. 
This  method  alone  should  be  employed  when  the  compared 
lights  differ  in  colour.  When  reading  the  field  under  such  cir- 
cumstances, it  is  essential  that  the  attention  should  not  be 
directed  toward  the  adjacent  portions  12  and  r2,  but  it  should 
be  given  wholly  to  the  contrast  between  TI  and  12,  and  r2  and  llf 
else  the  observer  will  become  confused  and  be  unable  to  deter- 
mine a  position  corresponding  to  a  balance  between  the  illum- 
inatioHS  from  the  light  sources.  After  each  setting  the  sight 
box  should  be  reversed  and  a  second  reading  taken. 

78.  Certain  advantages  and   faults  of  the  Lummer-Brodhun 
optical  train.  —  At  best  it  is  a  complicated  apparatus  and  re- 
quires careful  attention  to  details  in  its  operation.     The  mir- 


78  PHOTOMETRICAL   MEASUREMENTS 

rors,  absorbing  strips,  and  prisms  must  be  perfectly  clean  and 
the  several  parts  be  in  correct  adjustment.  The  contrast  prin- 
ciple demands  on  the  part  of  the  observer,  both  practice  and 
skill,  especially  with  differently  coloured  lights.  Should  the 
train  be  employed  with  an  equally  illuminated  field,  the  ap- 
paratus will  not  prove  as  sensitive  as  a  well-made  Bunsen 
screen. 

For  general  photometrical  practice  the  Bunsen  screen  is  not 
only  the  simplest,  but  has  proven  the  most  efficient  means  for 
comparing  lights  which  are  closely  similar  in  colour. 

For  purposes  of  investigation  and  in  practised  and  skilled 
hands  the  Lummer-Brodhun  Contrast  Train  is  an  admirable 
piece  of  apparatus,  but  will  yield  probably  no  better  results 
than  the  Bunsen  screen  under  similar  conditions,  except  when 
there  is  a  marked  difference  in  colour  to  be  dealt  with ;  then  the 
compact  field,  the  two  portions  adjoining  each  other,  presents 
a  decided  advantage.  The  fact  that  the  apparatus  is  monocu- 
lar causes  the  eye  to  fatigue  rapidly  and  is  confusing  in  form- 
ing a  judgment  of  contrasts.  The  mirrors,  too,  are  a  fruitful 
source  of  derangement ;  for  unless  they  are  identical  in  reflect- 
ing power,  neither  an  equally  illuminated  field  nor  equal  con- 
trasts can  be  obtained.  In  an  improved  form  of  the  apparatus 
the  mirrors  are  replaced  with  totally  reflecting  prisms,  thus 
increasing  not  only  the  reliability  but  the  sensitiveness  of  the 
apparatus. 

THE  LEONHAKD  WEBER  PHOTOMETER* 

79.  This  valuable  apparatus  may  be  readily  understood  if  it 
is  regarded  as  a  development  of  a  photometer  based  on  a  trans- 
mitting diffusion  screen.  For  this  discussion,  the  Joly  screen 
(page  90)  of  two  opal  glass  parallelepipedons  is  well  adapted. 

*  Leonhard  Weber,  Wiedemann's  Annalen  ;  20,  1883,  page  326  ;  and 
the  Elektrotech.  Zeitschrift,  1894,  page  166.  Also  R.  O.  Heinrichs, 
Transactions  American  Institute  of  Electrical  Engineers ;  11,  1894,  page 


PHOTOMETERS  79 

Imagine  the  glass  block  facing  the  compared  light  to  be  fixed 
in  position,  and  its  mated  block  to  be  movable  toward  or  from 
the  standard  light.  If  some  optical  device  were  interposed  to 
combine  the  two  diffused  fields  into  one  consecutive  field,  the 
illumination  from  the  lights  could  be  as  nearly  balanced  as  in 
the  accepted  arrangement  of  the  Joly  screen. 

Taking  the  distance  of  the  fixed  block  from  its  light  source 
as  L,  and  that  of  the  movable  one  as  I  the  usual  photometrica'l 
law  would  apply, 

/'=!/.  (56) 

Further,  suppose  the  diffusing  blocks  are  not  similar,  but 
designedly  possess  different  coefficients  of  absorption  of  the 
light  passing  through  them.  If  they  are  calibrated  to  com- 
pensate for  this,  and  their  experimentally  known  relation  is 
expressed  by  the  constant  C,  and  if  /  is  unity,  equation  56 
reads, 

r=clf>  (57) 

which  is  in  fact  the  general  form  of  the  working  equation  of 
the  Weber  photometer. 

This  apparatus  consists  of  a  tube  A  (Fig.  28),  which  is 
mounted  horizontally  and  is  attached  to  a  sleeve  sliding  on  a 
stout  post  screwed  into  the  top  of  the  containing  case.  The 
tube  contains  a  circular  opal  glass  plate  /,  which  is  movable 
by  a  rack  and  pinion  worked  by  the  milled  head  v ;  and  to  this 
member  is  attached  an  index  finger,  which  moves  over  an 
appropriate  scale  placed  on  the  outside  of  the  tube.  The  pho- 
tometer settings  are  accomplished  through  this  mechanism. 

A  lamp  case  slips  on  the  larger  end  of  this  tube,  in  which  is 
placed  the  standard  light.  The  other  end  carries  a  sleeve 
upon  which  is  centred  the  tube  JB,  whose  axis  is  at  right 
angles  to  that  of  the  tube  A.  The  sleeve  is  provided  with  a 
clamping  device  i,  for  holding  the  tube  at  any  desired  angle  of 


80 


PHOTOMETRIC AL  MEASUREMENTS 


inclination.     A  divided  sector  and  index  finger  are  placed  here 
to  indicate  the  inclination  of  the  tube. 

A  Lmnmer-Brodhun  contrast  prism  (page  76)  is  mounted  in 
the  second  tube  at  p,  while  at  the  smaller  end  o  is  located  a 
telescopic  eyepiece  for  viewing  the  optical  screen.  This  eye- 
piece is  slotted  to  receive  a  slide  with  three  circular  openings ; 
one  of  these  is  left  blank  while  the  others  are  filled  with  thin 
plates  of  red  and  green  glass  respectively.  The  other  end  of 
the  tube  is  fitted  with  a  flat  and  square  box  g,  in  which 


FIG.  28. 


opal  or  coloured  glass  plates  may  be  inserted,  and  it  is  sur- 
mounted by  a  narrower  tube  k,  for  the  admission  of  the 
measured  light. 

A  small  prism  s  may  be  attached  to  the  eyepiece  to  enable 
the  screen  to  be  viewed  when  the  tube  is  pointed  upward. 

The  standard  light  is  obtained  from  a  benzine  lamp.     The 


PHOTOMETERS  81 

lamp  is  a  long  and  slender  tube,  constricted  to  a  narrow  opening 
for  the  wick.  The  wick  is  manipulated  by  a  bent  hook 
attached  to  a  sliding  rod.  A  scale  and  a  sighting  device  are 
placed  in  the  lamp  case  to  enable  the  flame  height  to  be 
adjusted  with  great  precision. 

The  combustible  used  in  this  lamp  is  benzine,  which  should 
be  as  pure  as  possible ;  and  since  the  benzine  flame  must  itself 
be  standardized  against  an  amyl  acetate  or  pentane  flame,  it  is 
well,  when  beginning  measurements  with  this  instrument,  to 
provide  several  gallons  of  benzine  of  like  quality,  and  care- 
fully bottle  it  for  subsequent  use.  In  this  manner  a  uniform 
quality  of  the  combustible  will  be  maintained,  and  it  will 
obviate  frequent  calibration  of  the  flame. 

The  lamp  is  removed  for  filling,  and  after  being  lighted,  is  at 
once  slipped  into  position.  It  should  be  allowed  to  burn  for 
ten  or  fifteen  minutes,  when  the  flame  will  become  practically 
constant. 

When  a  measurement  is  to  be  made,  the  flame  should  be 
adjusted  to  a  standard  height  of  20  millimetres  with  great 
exactness;  and  in  all  cases  the  precise  height  of  the  flame 
should  be  noted  at  the  moment  of  measurement.  A  deviation 
of  0.1  millimetre  in  the  height  will  correspondingly  alter  the 
value  of  the  light  source  by  nearly  one  per  cent.  A  correction 
may  be  applied  for  any  deviation  within  one  millimetre,  of  one 
per  cent  for  each  0.1  millimetre  deviation  from  standard  height ; 
the  correction  being  added  for  an  excess  over  the  normal  and 
subtracted  for  a  deficit. 

A  compound  woven  wick  is  used,  the  upper  portion  being 
woven  from  asbestos  fibre,  and  it  must  be  kept  thoroughly 
clean.  After  trimming  the  wick,  it  should  be  lightly  pressed 
between  the  fingers,  and  projecting  fibres  are  to  be  carefully 
avoided. 

A  white  screen,  coated  with  a  wash  of  magnesium  oxide,  or 
some  similar  substance,  and  about  one  foot  square,  is  one 
of  the  included  accessories.  This  adjunct  is  employed  in 
the  measurement  of  diffused  illumination,  and  in  determining 


82  PHOTOMETRICAL  MEASUREMENTS 

the  constants  of  the  instrument.  When  in  use  it  is  mounted 
on  a  separate  stand  provided  for  it. 

The  operator  must  be  assured  that  the  diffusing  plates  and 
the  colour  screen  in  the  eyepiece  are  perfectly  clean,  before 
beginning  the  measurements. 

This  photometer  is  compact  and  portable,  and  is  especially 
adapted  for  measuring  the  intensity  of  illumination  from 
diffused  daylight  or  from  artificial  sources,  and  as  well  the 
illuminating  power  of  light  sources.  It  is  one  of  the  most 
accurate  and  convenient  means  for  exploring  the  illumination 
of  large  rooms  or  the  lighting  of  streets. 

The  comparing  tube  k  may  be  turned  to  any  point  in  azimuth 
or  altitude,  so  that  whatever  the  position  of  the  source 
measured  may  be,  the  tube  can  readily  be  pointed  toward  it. 
This  flexibility  renders  the  photometer  suitable  for  exploring 
the  distribution  of  the  illuminating  intensity  about  a  light 
source.  For  this  purpose  the  photometer  may  be  mounted  on 
a  rectangular  frame  (page  237)  to  travel  about  the  light  source 
as  a  centre ;  or  being  kept  stationary,  the  compared  light  may 
be  moved  about  the  photometer.  It  may  even  be  located  as 
near  an  arc  lamp  under  measurement  as  one  metre,  by  placing 
additional  glass  plates  in  the  slot  g. 

80.  The  applications  of  the  Weber  photometer.  —  There  are 
three  general  cases  into  which  the  practice  with  this  apparatus 
falls: 

I.  TJie  measurement  of  the  luminous  intensity  of  primary 
light  sources,  having  the  same  quality  of  light  as  the  benzine 
jlame. 

A  diffusing  glass  plate  of  appropriate  opacity  is  placed  in 
the  slot  g,  and  the  tube  Jc  is  turned  directly  toward  the  light 
source.  The  position  of  the  plate  /  in  the  tube  A  is  then 
adjusted  by  turning  the  milled  head  until  the  sight  field 
appears  uniformly  lighted  to  the  observer,  placing  the  eye  at 
0.  The  distance  L  in  centimetres  is  then  measured  from  the 
centre  of  the  light  source  to  the  diffusing  plate  at  g}  and  the 


PHOTOMETERS  83 

scale  reading  on  the  tube  A  will  state  the  distance  Z,  also  in 
centimetres  from  the  plate  /  to  the  centre  of  the  benzine  flame. 
The  intensity  / '  of  the  light  source,  is,  then, 

/'=  C~  light  units.  (57  bis) 

The  value  of  the  constant  C  corresponding  to  the  particular 
plate  used  in  g,  is  taken  from  a  table  furnished  by  the  maker, 
or  it  may  be  determined  by  the  observer. 

The  value  of  I  should  not  be  less  than  10  centimetres,  or  the 
plate  screen  will  be  placed  too  close  to  the  flame  for  accurate 
setting.  Should  a  balance  not  be  obtained  with  I  in  excess  of 
10  centimetres,  two  or  more  plates,  giving  increased  opacity, 
may  be  inserted  at  g.  The  makers  provide  from  three  to  four 
such  plates  with  various  degrees  of  opacity. 

The  lights  compared  being  of  the  same  colour,  the  field  may 
be  viewed  through  the  red  or  green  glass  in  the  ocular,  or  using 
neither,  as  the  field  can  be  accurately  balanced  in  any  case. 

II.  TJie  measurement  of  the  intensity  of  a  secondary  source  of 
illumination ;  the  diffused  light  having  the  same  colour  as  the  ben- 
zine flame. 

(1)   By  the  use  of  the  white  screen. 

The  tube  k  being  still  in  place,  no  glass  plate  is  needed  at  g, 
as  diffusion  is  accomplished  by  the  white  screen,  unless  the 
intensity  of  the  illumination  is  too  great  to  obtain  a  balance. 
The  distance  of  the  white  screen  from  the  instrument  is  not 
material  so  long  as  the  edges  of  the  screen  lie  well  without  the 
maximum  cone  of  rays  which  can  enter  the  tube  Jc.  This  may 
be  readily  determined  by  removing  the  tube  and  holding  it  in 
the  relative  position  toward  the  screen  which  it  will  occupy 
when  the  photometer  is  finally  adjusted,  and  viewing  the  screen 
through  it.  The  screen  may  be  placed  at  any  desired  angle 
with  reference  to  the  axis  of  the  tube  B  so  long  as  its  obliquity 
does  not  exceed  60°  from  the  normal  to  the  photometer. 

The  photometrical  reading  is  made  as  in  the  first  case,  and 


84  PHOTOMETRIC  AL   MEASUREMENTS 

the  intensity  of  the  diffused  illumination,  Z>,  is  calculated  from 
the  formula, 


D  =          C'  metre-light-units.  (58) 

If  the  light  unit  used  in  the  determination  of  C'  is  the  candle 
(English  or  German),  the  result  will  be  in  terms  of  the  candle- 
metre.  In  any  case  the  value  of  C'  is  found  by  placing  the 
standard  of  light  100  centimetres  from  the  white  screen. 
Should  a  balance  not  be  obtained  without  a  plate  interposed  at 
g,  appropriate  plates  may  be  inserted  and  the  corresponding 
constant  CV,  or  CJ,  etc.,  employed. 

(2)  A  ground  opal  glass  plate  is  employed  instead  of  the  white 
screen. 

The  photometer  may  be  made  entirely  self-contained  for 
such  measurements  by  removing  the  tube  k  and  placing  a 
ground  opal  glass  plate,  usually  marked  /u,  by  its  makers,  on 
the  end  of  the  tube  to  close  the  opening  at  g.  The  photometer 
is  then  disposed  so  that  the  ground  glass  plate  will  occupy  the 
exact  position  of  the  white  screen  had  it  been  used. 

The   intensity  of  the   illumination   is  then   given  by   the 

formula,  -i  n/y> 

D  =  ^-C",  (69) 

where  C"  is  a  new  constant  determined  under  the  condition 
here  employed;  but  additional  plates  may  be  inserted  at  g  as 
before,  when  the  constant  will  correspondingly  change  to  the 
value  d"  or  <72",  etc. 

The  constants  of  a  Weber  photometer  used  in  the  author's 
laboratory  were  :  — 

I.   FOR  PRIMARY  LIGHT  SOURCES 


Diffusing  Plate 

Constant 

Value  of  Constant 

Number  3 

C 

0.4175 

3  +  4 

cl 

1.375 

3  +  4  +  5 

C2 

3.519 

PHOTOMETERS 


85 


II.   FOB  DIFFUSED  ILLUMINATIONS 


Diffusing  Plate 

Constant 

Value  of  Constant 

No  plate  used 
Number  1 

a 

C' 

0.1332 
0.8978 

2 

C'2 

11.57 

3 

C"3 

17.64 

3  +  4 

c\ 

57.23 

3  +  4  +  5 

C's 

146.5 

III.   WITH  GROUND  OPAL  GLASS  PLATE 


Additional  Diffusing  Plate 

Constant 

Value  of  Constant 

fj.  used  alone 

C" 

0.7119 

M  +  3 

C  " 

6.471 

M  +  3  +  4 

C*  lf 

19.62 

M+3+4+5 

Cft 
3 

47.43 

III.  For  measurements  when  the  colour  of  the  light  source 
differs  from  that  of  the  standard  flame* 

The  illuminating  power  of  the  blue  rays  for  purposes  of  dis- 
tinct vision  of  lines  or  print  is  low  in  comparison  with  that  of 
the  other  colour  groups  of  the  spectrum.  If  light  sources  then 
differ  in  colour  to  such  an  extent  that  they  can  not  be  directly 
compared,  a  fairly  satisfactory  comparison  —  a  working  com- 
parison rather  than  a  scientific  one  —  may  be  made  between 
their  red  and  green  colour  constituents ;  and  from  these  com- 
parisons a  relation  may  be  established  for  expressing  the 

*  This  method  is  based  on  the  investigations  of  Purkinje,  and  especially 
of  Le"pinay  ;  "  On  the  Photometry  of  Colored  Lights,"  Annalesde  Chemie 
et  de  Physique,  (5),  24,  1881,  pages  289-337;  and  "The  Photometric 
Comparison  of  Different  Parts  of  the  Same  Spectrum,"  (5)  30,  1883, 
pages  145-214. 


86  PHOTOMETEICAL   MEASUEEMENTS 

illuminating  power  of  the  one  light  source  in  terms  of  the 
other  one. 

This  is  admissible  only  when  the  lights  compared  have 
similar  spectral  groups,  and  the  lights  vary  rather  in  the  rela- 
tive intensity  of  their  colour  groups.  The  practice  of  the 
method  applies  between  hydrocarbon  flames  and  the  incandes- 
cent or  arc  lights ;  but  can  not  be  successfully  employed  be- 
tween these  and  the  incandescent  gas  mantles  or  daylight. 

Either  the  illuminating  power  of  a  primary  light  source  may 
be  determined  in  this  manner  or  the  diffused  illumination  from 
a  secondary  source. 

The  manipulation  of  the  photometer  for  differently  coloured 
lights  follows  the  practice  already  outlined.  Two  observations 
are  needed :  in  one  the  lights  are  balanced  by  viewing  the  field 
through  the  red  glass,  in  the  other  through  the  green  glass 
plates  in  the  ocular.  The  intensities  are  calculated  by  formula 
57,  as  before.  The  intensity  found  by  the  use  of  the  red 
glass,  denoted  by  R,  is  combined  with  the  intensity  Gr  found 
with  the  green  glass,  through  a  factor  K,  in  .order  to  finally 
express  the  illuminating  intensity  sought.  Thus, 

/"  =  RK.  (60) 

The  factor  K  of  the  formula  assumes  a  new  value  for  each 

Gr  Gr 

particular  value  of  the  ratio  — •    The  relation  between  —  and 

H  H 

K  may  be  determined  experimentally,  and  tabulated  for  the 
practice  of  the  method. 

An  example  will  make  this  somewhat  complicated  process 
clear.  With  the  red  glass  used,  a  balance  was  obtained  with  a 
scale  reading  I,  of  15  centimetres;  the  compared  light,  an 
incandescent  lamp  was  placed  at  a  distance  of  100  centi- 
metres from  the  plate  g.  From  formula  57,  with  a  value  for 
C  of  0.33,  the  intensity  R  =  IJ  is 

R  ==  //  =  0.33  ^M2  =  14.7  light  units  of  visibility. 


PHOTOMETERS  87 

Similarly  with  the  green  glass  I  was  13.5  centimetres.    Then 


Gr  =  IJ  =  0.33         9  =  18.1  light  units  of  visibility. 
13.5 


From  a  table  the  value  of  K  corresponding  to  the  ratio  1.23 
is  1.17.  Finally  the  intensity  sought  is 

/"  =  14.7  x  1.17  =  17.2  light  units. 

This  number  represents  the  measure  of  the  illuminating 
power  of  the  source,  for  distinctness  of  vision  referred  to  the 
like  illuminating  power  of  the  standard  German  candle. 

Such  practice  with  the  Weber  photometer  gives  results 
closely  resembling  those  obtained  by  spectrophotometry,  ex- 
cept that  they  are  less  general  and  exact. 

These  same  results  may  be  more  simply  and  directly  ob- 
tained by  the  use  of  a  flicker  photometer;  though  this  pho- 
tometer lacks  the  peculiar  portability  of  the  Weber  apparatus. 
When  measurements  can  be  carried  out  in  the  photometrical 
laboratory,  the  nicker  photometer  commends  itself,  but  for  the 
study  of  light  sources  in  their  position  of  actual  use,  the 
Weber  photometer  is  practically  the  more  available  apparatus. 

81.  The  determination  of  the  constants.  —  Though  such  data 
are  supplied  by  the  maker,  they  may  be  readily  found  or 
checked  by  the  observer.  To  this  end  a  known  light  source  is 
required,  whose  colour  is  similar  to  that  of  the  benzine  flame. 
It  may  be  a  pentane  or  other  hydrocarbon  flame,  or  an  incan- 
descent lamp  ;  the  amyl  acetate  flame  is  too  red  to  use  directly. 
In  any  case  the  illuminating  power  of  the  flame  employed  is 
carefully  determined  by  the  usual  photometrical  methods. 

If  such  a  light  source  is  employed  according  to  the  methods 
of  cases  I  or  II,  the  value  of  the  constants  (7,  or  C",  etc.,  is 
found  at  once  by  solving  for  it  in  formula  57. 


88          PHOTOMETRICAL  MEASUREMENTS 

The  value  of  K  has  been  calculated  for  the  usual  light  com- 
parisons,* and  appropriate  tables  are  included  with  a  record  of 
the  constants  of  the  photometer.  While  the  determination  of 
this  factor  is  tedious,  it  may  be  accomplished  in  the  ordinarily 
equipped  laboratory. 

The  use  of  such  an  obscure  factor  is  undesirable  since  all  the 
conditions  of  the  measurement  are  not  within  the  immediate 
control  of  the  observer,  and  results  at  best  carry  with  them  an 
element  of  uncertainty.  No  measurement  can  be  regarded  as 
either  practical  or  strictly  scientific  until  all  the  conditions  and 
factors  entering  into  it  are  under  the  immediate  knowledge  or 
control  of  the  investigator  or  practician. 

Lepinay  f  found  for  light  sources  having  the  same  tempera- 
ture but  different  emissive  powers,  a  relation  which  is  ex- 
pressed by 

T  /rt~\ 

(61) 


R     *  \R 

in  which  /  is  the  intensity  of  the  visibility  of  the  light  source. 
In  order  to  reduce  this  to  specified  practice,  he  adopted 
standard  red  and  green  light  screens  and  determined  the  real 
value  of  the  function.     For  one  set  of  screens  this  was, 

-  -  1  =  0.208  fl  -  — \  (62) 

an  expression  from  which  the  working  values  of  K  may  be 
calculated. 

This  photometer  has  been  discussed  at  some  length  on 
account  of  its  wide  range  of  practical  usefulness.  No  other 
instrument  is  so  peculiarly  adapted  for  measuring  the  inten- 
sity of  powerful  light  sources,  such  as  search  lights  and  the 
common  forms  of  the  arc  light.  Its  accuracy  is  enhanced  and 
its  range  is  increased  by  substituting  a  small  incandescent 

*  An  account  of  the  determination  and  a  table  of  values  are  given  in 
the  Elektrotech.  Zeitschrift,  1884,  pages  166-171. 
f  Comptes  Rendus  ;  97,  page  1428. 


PHOTOMETERS  89 

lamp  of  one  or  two  candle  power,  operated  by  a  portable  stor- 
age battery,  for  the  standard  benzine  flame.  The  filament 
should  lie  flat  in  a  plane  which  intersects  the  axis  of  the  socket 
on  which  the  lamp  is  mounted.  It  must  be  accurately  re- 
placed in  the  photometer  in  the  position  it  took  when  the 
constants  were  determined. 

The  intensity  of  such  a  standard  lamp  is  readily  calculated 
from  a  known  standard  by  the  use  of  the  photometer  itself, 
provided  the  diffusing  constants  (7,  C ',  or  C "  are  known. 


WEDGE-SHAPED  DIFFUSING  PLATES 

82.  The  action  of  diffusing  plates  in  relation  to  photometrical 
balancing  of  lights  has  been  defined  in  the  discussion  of  the 
Weber  photometer,  but  several  interesting  modifications  deserve 
attention. 

Sabine*  has  employed  a  wedge  of  neutral-tinted  glass,  A 
(Fig.  29),  for  an  absorption  plate,  which  was  compensated  for 
refraction  by  a  similarly 
shaped  wedge  of  clear  glass, 

1          •  -I          1    1 

B,  the  two  being  held  to- 
gether either  by  a  frame  or 
Canada  balsam.  This  com- 
pound plate  was  then  moved 
before  a  slot  C  in  an  opaque  FlG  29. 

diaphragm  by  a  screw  mo- 
tion, and  its  position  under  the  slot  was  recorded  by  a 
suitable  scale  which  was  calibrated  by  working  the  wedge 
with  lights  of  known  intensity,  so  that  the  amount  of  absorp- 
tion for  any  position  could  be  obtained  by  reference  to  the  scale 
reading. 

Sabine  employed  this  device  in  a  special  form  of  illumination 
photometer,  though  it  may  be  used  equally  well  on  any  pho- 
tometer bench. 

*  Philosophical  Magazine  ;   15,  1883,  page  22. 


90 


PHOTOMETRICAL   MEASUREMENTS 


83.  The  compensated  wedge.  —  The  principle  of  the  single 
absorption  wedge  is  open  to  the  objection  of  unequal  action  on 
the  incident  beam  of  light.  In  case  the  width  of  the  opening 
ab  (Fig.  29)  is  considerable  with  reference  to  the  slope  of  the 
wedge,  that  portion  of  the  light  transmitted  nearest  6  will  be 
brightest,  and  the  intensity  will  be  regularly  diminished  toward 
a.  If  all  the  transmitted  light  were  to  be  blended  or  focussed 
on  the  screen,  this  would  have  no  significance  aside  from  a  prob- 
able change  in  the  quality,  due  to  selective  absorption.  The 
light,  however,  is  reflected  from  the  screen,  as  it  is  transmitted 
to  the  wedge,  with  the  result  of  an  unequally  illuminated  field. 


FIG.  30. 


This  defect  is  neatly  corrected  by  Spitta  *  through  a  compen- 
sating compound  wedge  (Fig.  30).  This  consists  of  two 
wedges,  similar  in  all  respects,  which  by  sliding,  the  one  over 
the  other,  maintains  a  uniform  thickness  of  the  absorbing 
medium  throughout  the  width  of  the  slit.  The  action  of  the 
absorbing  medium  is  then  fairly  uniform,  except  for  a  constant 
loss  of  light  by  reflection  from  the  separating  planes  of  the 
wedge. 

THE   JOLY   DIFFUSING   SCREEN 

84.  Very  similar  to  the  Elster  diffusing  screen  is  that  de- 
vised by  Joly,t  though  with  an  added  optical  feature  which 
allies  it  with  both  the  Bunsen  and  the  Lummer-Brodhun 

*  Proceedings  Royal  Society  ;  47,  1889,  page  15. 
t  Philosophical  Magazine  ;  26,  1888,  page  26. 


PHOTOMETERS  91 

screens.  Structually,  it  is  the  Elster  screen  with  the  partition 
omitted. 

The  two  parallelepipeds  of  the  paraffine  cube  are  neatly 
smoothed  on  their  cut  faces,  and  these  are  closely  pressed 
together.  The  light  falling  on  each  half  will  illuminate  it  by 
diffusion.  Each  cut  surface  will  reflect  the  light  from  within 
the  mass  of  its  appropriate  half,  both  specularly  and  totally, 
thus  rendering  the  slit  darker  and  apparent.  A  portion  of  the 
light  from  each  half  passes  across  the  slit  into  the  other  half. 
When  the  two  blocks  are  equally  illuminated,  the  reflected  and 
transmitted  lights  are  balanced  in  each,  and  the  slit  becomes 
invisible.  The  cube  may  be  of  opal  glass  and  the  two  portions 
cemented  together  by  Canada  balsam. 

When  differently  coloured  lights  are  compared,  the  discon- 
tinuity between  the  diffused  lights  due  to  the  slit  does  not 
wholly  disappear.  Though  a  most  excellent  screen  for  com- 
paring lights  of  like  tint,  it  has  no  especial  advantage  over 
other  forms  when  the  lights  differ  in  colour.  Joly  mentions  the 
advantage  from  viewing  the  slit  with  a  magnifying  glass,  which 
enables  more  sensitive  settings  of  the  screen  to  be  made. 

This  compound  screen  may  be  mounted  in  a  sight  box  of  the 
usual  type,  blackened  on  its  interior.  The  dimensions  recom- 
mended for  the  two  parallelepipeds  were  20  x  50  x  11  milli- 
metres. 

THE   FLICKER   PHOTOMETER 

85.  It  has  been  insisted  upon  as  one  of  the  fundamental 
principles  of  photometry,  that  only  the  illuminations  of  similar 
colour  quality  could  be  accurately  compared.  While  this  is 
generally  admitted,  practice  will  frequently  present  occasions 
when  lights  differing  considerably  in  tint  must-  be  compared, 
such  as  the  light  given  by  a  Welsbach  mantle,  with  that  of  the 
ordinary  gas  flame ;  or  as  the  light  from  the  arc  with  that  from 
the  incandescent  lamp. 

The  only  basis  for  comparison  is  that  the  lights  differing  in 
tint  shall  produce  equally  intense  sensations  of  luminosity  for 


92 


PHOTOMETRICAL   MEASUREMENTS 


viewing  fine  lines  or  print.  But  this  involves  all  the  physio- 
logical and  subjective  difficulties  already  discussed. 

The  most  successful  apparatus  for  effecting  comparisons 
between  dissimilar  lights  is  the  flicker  photometer,  based  on 
presenting  to  the  eye,  surfaces  illuminated  by  each  light  source 
in  rapidly  alternating  succession  (consult  page  18). 

The  apparatus  may  be  variously  arranged.  A  long  shaft 
may  be  attached  to  the  photometer  bench,  for  rotating  a  sec- 
tored disk  before  each  light  source,  the  sectors  being  adjusted 
to  eclipse  each  light  in  succession.  Any  form  of  screen  may  be 
used  with  the  sectors,  though  a  Ritchie  or  a  Thompson  wedge 
is  especially  adapted  for  this  work. 

Whitman1*  has  designed  a  form  of  flicker  photometer  in 
which  the  sector  is  combined  with  the  reflecting  screen,  and  is 
thus  movable  with  the  sight  box. 


FIG.  31. 

A  disk  AHBG  (Fig.  31)  was  cut  from  cardboard,  the  radius 
of  the  semicircle  HBG  being  8  centimetres,  and  that  of  GAH 
being  5  centimetres.  This  was  mounted  on  a  shaft  K  attached 
to  the  sight  box,  and  rotated  before  the  similar  cardboard 
screen  (7,  in  such  position  that  the  part  B  should  eclipse  the 
fixed  screen  C  when  viewed  through  the  tube  F. 

The  screen  is  thus  in  effect  a  Thompson  wedge  with  one 

*  F.  P.  Whitman,  Physical  Review,  1896,  page  241. 


PHOTOMETERS  93 

side  only  projecting.  The  sequence  of  the  lights  and  sides  of 
the  screen  is  indifferent ;  though  a  notable  defect  of  the  pho- 
tometer is  that  the  screen  can  not  be  reversed.  The  sector  may 
be  rotated  by  hand  or  by  a  motor,  the  rotation  being  adjusted 
to  that  critical  speed  at  which  the  illumination  appears  con- 
secutive. Then,  when  the  intensity  of  the  illumination  of  the 
fixed  and  rotating  sides  of  the  screen  differs,  though  the 
illumination  is  consecutive  it  will  produce  the  characteristic 
nickering  light  sensation,  which  will  disappear  when  the  screen 
is  moved  to  a  position  where  the  two  illuminations  are  balanced. 

Whitman,  testing  the  precision  of  the  setting  for  contrasting 
colours,  including  the  whole  range  of  the  spectrum,  found  that 
such  an  apparatus  could  be  used  upon  lights  presenting  the 
widest  contrast  in  colour  with  an  accuracy  approaching  that  of 
the  ordinary  types  of  the  photometer  when  balancing  lights  of 
the  same  colour. 

Such  results  are  only  obtained  with  a  normal  eye,  and  when 
not  fatigued.  Should  the  eye  be  fatigued,  it  would  show  a 
differential  sensibility  toward  one  light  or  the  other. 

A  fruitful  source  of  error  in  this  method  arises  from  the 
Purkinje  effect  (page  26),  though  the  error  would  be  a  physical 
rather  than  a  physiological  one. 

The  rapid  alternations  of  illumination  and  eclipse  of  the 
screen  tend  to  exercise  the  eye  at  its  maximum  sensitiveness ; 
and  for  a  similar  reason  would  decrease  the  difference  of 
settings,  or  the  personal  variable  between  observers. 

In  general  this  apparatus  requires  a  strong  illumination  of 
the  screen  in  order  to  operate  it  effectively. 

Experiments  have  shown  that  the  disk  need  not  be  equally 
divided;  and  that  irregularities  in  the  size  of  the  opening,  or 
the  rate  of  rotation,  are  without  appreciable  effect  on  the  set- 
ting of  the  screen.  This  apparatus  is  a  development  from  the 
investigations  by  Kood.* 

*  Rood,  American  Journal  of  Science  ;  46,  1893,  page  173  ;  also  Science  ; 
7,  1898,  page  757.  Whitman,  Science  ;  8,  1898,  page  11.  Ferry,  Ameri- 
can Journal  of  Science ;  44,  1892,  page  198. 


94 


PHOTOMETRICAL  MEASUREMENTS 


A  compact  and  highly  ingenious  form  of  the  nicker  pho- 
tometer has  recently  been  devised  by  Rood.*  It  is  shown  in 
plan  in  Figure  32.  The  screen,  P,  is  a  rectangular  prism  made 
from  plaster  of  Paris,  cast  in  a  mould  of  glass  plates  ground  to 
the  closest  fit  at  their  juncture,  that  the  working  edge  of  the 
prism  may  be  as  sharp  and  regular  as  possible  ;  otherwise  the 
edge  will  appear  in  the  field  as  a  vertical  black  line,  and  of 
itself,  will  produce  a  faint  flicker  that  will  persist  when  the 
flicker  from  the  faces  of  the  prism  has  disappeared. 


FIG.  32. 

A  concave  cylindrical  lens,  (7,  in  this  case  of  13  centimetres 
focus,  and  4  centimetres  square,  is  mounted  on  the  top  of  an 
oscillating  bar,  and  centred  with  reference  to  the  plane 
through  the  apex  of  the  prism  at  right  angles  to  the  photo- 
metrical  axis.  The  oscillating  bar  is  pivoted  in  the  base  of  the 
photometer  bench.  The  observing  tube,  T,  is  21  centimetres  in 
length,  and  4  in  diameter,  and  is  placed  coaxially  with  the 
normal  axis  of  the  oscillating  lens;  each  end  of  the  tube  is 
closed  with  a  diaphragm  pierced  with  an  aperture  5  milli- 
metres in  diameter. 

The  light  sources  compared  are  at  L  and  L1 ;  and  the  posi- 
tion of  the  standard  light  is  fixed,  while  the  compared  light  is 
moved  to  obtain  the  balance  between  the  illuminations. 

*  Ogden  N.  Rood,  "On  the  Flicker  Photometer,"  American  Journal  of 
Science,  8  September,  1899,  page  194  ;  and  "On  Colour  Vision  and  the 
Flicker  Photometer,"  October,  1899,  page  258. 


PHOTOMETERS  95 

The  oscillating  bar  is  moved  through  a  train  of  geared 
•wheels,  W,  actuated  by  a  small  electric  motor,  E,  which  is 
regulated  in  speed  by  means  of  a  suitable  rheostat,  R ;  while 
D  is  a  speed  indicating  disk  provided  with  a  number  of  black 
and  white  sectors,  the  device  being  adjusted  to  indicate  the 
proper  frequency  of  oscillation  of  the  lens  through  the  blend- 
ing of  the  sectors. 

The  maximum  sensitiveness  of  this  photometer  follows  the 
adjustment  which  will  produce  the  strongest  flicker;  and  as 
this  is  dependent  only  on  the  frequency  of  the  oscillations  of 
the  lens,  the  best  condition  results  when  the  two  illuminated 
faces  of  the  prism,  P,  are  just  blended  by  the  movement 
of  the  lens.  Eood  found  a  frequency  of  oscillation  of  the 
lens  of  16  to  the  second  would  produce  the  maximum  sensitive- 
ness. 

This  apparatus  is  a  departure  in  the  means  for  produc- 
ing the  flicker  though  in  all  essential  respects  its  operation 
follows  the  method  already  described  for  the  flicker  photom- 
eter. 

The  illumination  of  the  sides  of  the  screen  was  varied  in 
quality  by  inserting  coloured  glass  plates,  GG'.  In  this  man- 
ner a  large  number  of  experiments  were  made,  comparing 
lights  whose  colours  differed  widely,  with  the  "  general  con- 
clusion drawn  from  numerical  results  that  the  accuracy  attain- 
able with  the  flicker  photometer,  as  at  present  constructed,  and 
using  lights  of  different  colours  almost  spectral  in  hue,  is  about 
the  same  as  with  ordinary  photometers  using  plain  white  light, 
or  light  of  exactly  the  same  colour." 

THE    ILLUMINATION    PHOTOMETER    OF    PREECE    AND 
TROTTER 

86.  In  the  various  types  of  the  compact  or  self-contained  and 
portable  photometers,  advantage  has  been  taken  of  absorption 
or  dispersion  to  replace  the  usual  method  of  the  variation  of 
the  illumination  from  the  standard  light,  by  increasing  the 


96 


PHOTOMETRICAL   MEASUREMENTS 


distance  between  it  and  the  screen.  However,  W.  H.  Preece 
and  A.  P.  Trotter*  have  developed  an  unusually  compact 
instrument  for  measuring  the  intensity  of  illumination  by 
varying  the  standard  illumination  according  to  Lambert's 
cosihe  law  (see  page  33). 

The  containing  case,  Figure  33,  is  a  light-proof  box  blackened 
on  its  interior.  At  the  end  marked  L,  two  small  incandescent 
lamps  are  attached,  of  one  and  two  candle  power  at  twelve 
volts.  These  are  lighted  by  a  portable  storage  battery. 


FIG.  33. 


Two  screens  are  employed ;  the  diffusing  screen  Z),  and  the 
comparison  screen  JS.  The  diffusing  screen  D  is  a  sheet  of 
Bristol  board,  which  has  been  moistened  to  remove  all  glaze 
and  surface  finish,  and  is  hung  at  the  opposite  end  of  the  box 
from  the  lamps.  It  is  essential  that  this  screen  shall  have  a 
regular  and  fairly  smooth  surface,  for  at  its  maximum  incli- 
nation when  the  light  is  incident  upon  it  at  an  angle  approach- 
ing 90°,  the  irregularities  would  be  plainly  visible  and  make 

*  Electrician  (London),  September  20, 1895.  For  an  extended  account 
consult  Proceedings  Institute  of  Civil  Engineers ;  35,  1883,  page  39,  and 
volume  110,  page  98. 


PHOTOMETERS  97 

accurate  readings  impossible.  The  maximum,  illumination 
occurs  when  the  angle  of  inclination  is  about  45° ;  and  at  this 
angle  any  glaze  on  the  surface  would  produce  specular  reflec- 
tion, leading  to  equally  inaccurate  readings.  A  suitable  sur- 
face for  the  screen  must  be  selected  under  these  limitations, 
and  it  has  been  found  especially  difficult  to  meet  these  require- 
ments and  not  depart  sensibly  from  the  cosine  law. 

The  centre  of  the  screen  is  about  eleven  inches  from  the 
lamps,  though  this  dimension  differs  with  the  inclination. 
The  screen  is  hinged  at  its  upper  end,  and  the  inclination  is 
effected  by  a  series  of  levers  and  links  operated  by  a  handle, 
with  an  attached  pointer  moving  over  a  graduated  scale. 

The  observing  screen  or  diaphragm  S,  is  located  on  the  top 
of  the  box  immediately  over  the  diffusing  screen.  It  is  perfo- 
rated by  three  star-shaped  openings.  One  opening  would  be 
sufficient,  but  the  sensitiveness  of  the  setting  is  increased  by 
the  added  contrast  with  the  two  equally  illuminated  openings, 
one  on  either  side.  When  the  compared  lights  agree  in  tint, 
either  the  outer  openings  or  the  central  one  may  be  made  to 
disappear,  though  it  is  designed  to  employ  the  disappearance 
of  the  central  opening.  When  the  compared  illuminations  are 
balanced,  it  is  evident  that  an  equal  flux  of  light  takes  place 
in  each  direction. 

For  similarly  coloured  lights  the  diaphragm  should  be  of  the 
same  material  as  the  inclined  screen,  with  the  same  surface 
tint ;  and  when  the  lights  are  dissimilar,  the  screen  surfaces 
should  still  be  alike  though  they  may  correspondingly  differ 
in  tint.  Instead  of  Bristol  board,  thin  sheets  of  metal  have 
given  good  results,  painted  with  a  wash  of  magnesium  oxide 
in  a  solution  of  isinglass.  For  comparing  the  illumination 
from  an  arc  light,  the  hinged  screen  may  be  tinted  pale  blue 
and  the  diaphragm  a  pale  yellow,  and  in  this  manner  the  star 
may  be  made  to  disappear.  Such  an  adjustment  yields  only 
approximate  results,  for  it  practically  halves  the  error  due  to 
dissimilarity  in  tints  between  the  lights,  and  requires  an  espe- 
cial calibration  of  the  scale. 


98  PHOTOMETRICAL  MEASUREMENTS 

The  scale  is  direct  reading,  and  is  calibrated  empirically 
under  known  standard  conditions.  Its  intervals  depart  from 
the  cosine  law  through  the  peculiar  adjustment  of  the  levers 
and  the  departure  of  the  screen  itself,  for  mechanical  reasons, 
from  the  formal  law  of  reflection.  The  scale  unit  is  the  candle- 
foot,  and  the  highest  reading  is  unity  with  the  smaller  lamp 
lighted,  and  all  its  indications  are  fractional. 

Increased  range  is  given  by  the  use  of  two  lamps,  either  of 
which  or  both  may  be  employed ;  the  larger  one  giving  results 
of  double,  and  the  two  combined  of  three  times  the  direct  scale 
values. 

To  operate  the  photometer,  one  or  both  lamps  are  lighted, 
the  observer  views  the  screen  in  the  vertical  plane  of  the  three 
holes,  and  the  handle  is  moved  until  the  middle  star  disap- 
pears if  the  lights  are  of  similar  tint;  or,  should  the  lights 
differ  in  tint,  the  screen  is  moved  rapidly  back  and  forth  until 
a  new  setting  is  obtained.  The  value  of  the  illumination  in  the 
candle-foot  unit  (page  37)  is  then  read  directly  from  the  scale. 

87.  The  illuminometer  of  Houston  and  Kennelly.*  —  This 
apparatus  was  designed  to  measure  directly  the  degree  of 
illumination  at  any  desired  point.  The  containing  case  is 
fitted  with  a  sight  tube  and  magnifying  eyepiece  E  (Fig.  34), 
which  focusses  on  the  inclined  surface  at  B  carrying  the  test 
object,  which  may  be  white  paper  with  printing  or  drawing 
upon  it.  The  test  object  is  illuminated  through  the  opal-glass 
window  Wj  while  the  effective  area  of  the  window  is  controlled 
by  the  sliding  shutter  S,  whose  movement  is  indexed  along  an 
appropriate  scale. 

The  eyepiece  having  been  focussed,  the  shutter  is  opened 
until  the  test  object  becomes  clearly  visible,  when  the  degree 
of  illumination  may  be  read  directly  from  the  scale.  Instru- 
mentally,  the  degree  of  illumination  is  a  function  of  the 
effective  area  of  the  opal  glass  window.  The  scale  is  calibrated 
in  the  photometer  dark  room,  from  a  light  whose  illuminating 

*  Electrical  World ;  25,  1895,  page  309. 


PHOTOMETERS 


99 


power  is  known,  by  placing  the  apparatus  at  measured  distances 
and  marking  the  position  of  the  shutter  at  which  the  test  object 
becomes  visible.  The  scale  unit  is  then  the  candle-metre 
(page  37). 

Owing  to  the  fatigue  of  the  eye,  there  will  be  some  dis- 
crepancy in  the  readings  made  by  obscuring  the  window  from 
full  illumination  until  the  test  object  disappears,  as  against 
readings  made  with  the  reverse  process. 

In  principle,  the  ilium inometer  is  a  photometer  in  which  the 
intensity  of  the  measured  illumination  is  compared  with  a 
standard  one,  —  that  under  which  the  scale  was  calibrated. 


W 


VWV^AAAAAA/U \S 


FIG.  34. 


The  vanishing  point  for  distinct  vision  is  neither  constant  in 
any  one  eye,  nor  is  it  the  same  between  different  eyes.  The 
sensitiveness  of  the  eye ,  too,  for  very  weak  light  is  low,  and 
these  two  causes  render  the  readings  of  the  instrument  indic- 
ative rather  than  quantitative.  The  designers  suggest  that 
the  mean  error  is  about  ten  per  cent. 

88.  The  relative  sensitiveness  of  photometer  screens.  —  Com- 
parative data  of  the  sensitiveness"  of  different  screens  are  to  be 
taken  as  suggestive  rather  than  final.  So  much  depends  on 
the  subjective  states  of  the  observer  as  well  as  the  care  in 
adjusting  lights  to  equal  tints,  upon  which  condition  the  com- 
parison is  based,  and  to  the  maintenance  of  the  lights  at 
constant  intensities. 


100  PHOTOMETRIC AL  MEASUREMENTS 

The  results  of  tests  by  the  Netherlands  Gas  Commission,* 
apparently  made  with  great  care,  are  of  value.  This  Com- 
mission found  the  average  settings  to  depart  from  a  true  mean 
value  by 

Per  Cent 

1.  For  Bunsen  Photometer,  ordinary  form  .  ±  0.08 

2.  Foucault  Photometer ±  0.32 

3.  Lummer-Brodhun  Optical  Screen       .        .        .        .         .  ±  0.52 

4.  Bunsen  Photometer  with  reflecting  prisms       .        .        .  ±  0.25 

VARIOUS  PHOTOMETERS  AND  PHOTOMETRICAL 
DEVICES 

89,  The  dispersion  lens.  —  A  concave  lens  placed  in  the  path 
of  the  light  from  a  source  will  disperse  it  over  an  increased 
surface,  whose  ratio  of  increase  of  area  over  that  which  would 
have  been  covered  by  the  unobstructed  light  is  determined  by 
the  radius  of  curvature  of  the  lens.      The  intensity  of  the 
resulting  illumination  will  vary  inversely  with  the  amount  of 
the  dispersion. 

The  method  is  apparently  a  simple  one  and  of  value  in 
photometrical  measurements,  but  in  practice  several  sources  of 
error  have  proven  the  method  an  unsatisfactory  one.  Except 
for  purposes  of  investigation,  it  is  now  seldom  employed,  and 
its  lessened  importance  does  not  warrant  a  full  discussion  of  its 
theory  in  this  connection.  Absorption  plates,  and  especially 
the  revolving  sector,  are  more  suitable  and  practical  means  for 
diminishing  the  intensity  of  the  radiations  from  a  light  source. 
The  objections  to  the  use  of  the  dispersion  lens  arise  from 
reflection  of  light  at  the  surface,  spherical  aberration,  and 
absorption  by  the  glass. 

90.  The   dispersion  photometer  of   Ayrton   and  Perry  f   was 
formerly  employed  to   a   considerable   extent,  but  it  offered 

*  Schilling's  Journal,  1894,  page  617. 
t  Philosophical  Magazine ;  14,  page  46. 


PHOTOMETERS 


101 


numerous  sources  of  error,  and  has  in  consequence  been  dis- 
placed by  more  accurate  apparatus.  However,  it  has  been  so 
widely  known  that  a  brief  description  will  be  given. 

The  photometer  mounts  a  biconcave  lens  in  the  frame  C 
(Fig.  35),  movable  along  the  slide  F.  A  reflecting  mirror  H,  is 
fastened  to  an  axis  at  a  fixed  inclination  of  45°,  and  enables  the 
light  from  a  source  placed  at  any  elevation  to  be  measured 
without  introducing  an  error  arising  from  absorption  at  vary- 
ing angles  of  reflection.  A  graduated  circle  G,  measures  the 


FIG.  35. 


angular  elevation  of  the  light  source.  A  standard  candle  is 
placed  in  a  case  which  prevents  its  light  from  falling  on  the 
side  of  the  screen  nearer  it;  the  containing  case  is  movable 
along  the  bar  J.  The  comparison  of  the  illuminations  is 
accomplished  by  means  of  a  Lambert  screen,  a  thin  black 
rod  being  mounted  in  front  of  a  sheet  of  white  paper  AB. 

The  distance  D,  of  the  compared  light  is  measured  to  the 
centre  of  the  mirror  H,  and  thence  to  the  screen.  The  distance 
d,  of  the  lens  from  the  screen  is  noted  as  well  as  the  distance 
c,  of  the  standard  candle.  The  focal  length  of  the  lens  being 


102  PHOTOMETRICAL  MEASUREMENTS 

/,  the  intensity  L,  of  the  compared  source  is  found  from  the 
formula  given  by  the  designers, 

(63) 


The  tedious  calculations  involved  in  this  method  greatly  inter- 
fere with  the  general  utility  of  the  apparatus.  The  formula 
contains  no  correction  factors  for  the  reflection  and  absorption 
of  the  light  by  the  lens,  and  at  best  can  only  be  an  approxi- 
mation. 

91.  The  intensity  of  the  illumination  in  terms  of  the  energy.  — 
The   complicated  nature   of    photometrical    observations   has 
already  been  emphasized  and  their  dependence  on  combined 
physical  and  physiological  events.     An  analogy  was  instituted 
in  Chapter  I  (page  3)  to  show  the  desirability  of  an  entirely 
physical   measurement   of  the  intensity  of  the  light  source, 
which  should  also  express  its  visual  intensity  ;  and  the  present 
seeming  impossibility  of  obtaining  this  consideration  was  dwelt 
upon. 

A  number  of  noteworthy  attempts,  however,  have  been  made 
to  accomplish  this  ;  but  they  have  resulted  only  in  a  measure- 
ment of  the  energy  of  the  illumination,  and  no  satisfactory 
factor  has  been  found  to  connect  this  with  the  visual  effect,  or 
to  translate  these  results  into  what  is  known  as  the  intensity 
of  the  illumination. 

92.  The  selenium  screen  is  such  an  attempt.     Light  falling 
on  selenium  changes   its   electrical   resistance   to   an   extent 
ascertained  by  Adams  *  to  be 


Resistance  of  Selenium  oc  V 'Illuminating  Power. 

Such  a  screen,  standardized  by  reference  to  a  known  light 
source,  may  be  mounted  on  the  photometer  bench  in  the  usual 
manner. 

*  Proceedings  of  the  Royal  Society  ;  28,  1876,  page  163  ;  also  Proceed- 
ings of  the  Institute  of  Civil  Engineers ;  44,  1876,  page  169. 


PHOTOMETERS  103 

93.  The  bolometer  *  is  an  apparatus  which  in  its  action  closely 
resembles  the  selenium  screen.     The  essential  portion  of  the 
apparatus  is  a  very  thin  wire,  usually  of  iron  coated  with  carbon. 
When  exposed  to  light  it  becomes  heated,  and  the  change  in  its 
electrical  resistance  affords  a  means  for  measuring  the  energy 
intensity  of  the  incident  light. 

94.  The  Crookes  radiometer,   shortly  after  its  development, 
was  investigated  as  a  probable  means  for  measuring  luminous 
intensity.     The  propulsion  of  the  vane  from  light  absorbed  on 
its  alternately  blackened  faces,  is  seemingly  a  direct  mechani- 
cal means  for  photometrical  measurements.     Pedler,t  investi- 
gating it  for  this  purpose,  found  that  the  temperature  of  the 
air  produced  such  marked  changes  in  the  rate  of  rotation  of 
the  vane,  that  from  this  cause  alone  it  would  not  prove  a 
practical  apparatus. 

95.  Chemical  photometry. — Numerous  attempts  have  been 
made  to  define  the  illuminating  power  of  a  light  source  in 
terms  of  its  activity  in  producing  certain  chemical  decomposi- 
tions.    The  chemical  action  of  light  is  largely  due  to  the  ultra- 
violet or  actinic  rays,  which  are  invisible.      A  light  source 
may  possess  a  high  illuminating  power  and  yet  be  very  feeble 
in  actinic  qualities;  and  conversely,  an  actively  actinic  light 
source  may  have  a  disproportionately  low  illuminating  power. 
There  being  no  essential  connection  between  the  proportion  of 
the  actinic  rays  and  those  producing  illumination,  the  applica- 
tion of  the  chemical  action  of  light  is  of  no  particular  value  in 
photometry. 

Draper  $  in  1859  endeavoured  to  measure  the  intensity  of 
daylight  by  its  action  on  a  solution  of  peroxalate  of  iron  and 

*  For  a  description  of  the  bolometer  and  its  application  to  photometri- 
cal measurements  consult  Transactions  of  the  American  Institute  of 
Electrical  Engineers,  13,  1896,  page  137. 

t  London  Journal  of  Gas  Lighting  ;   36,  1880,  page  335. 

J  Philosophical  Magazine  ;  May,  1859,  page  91. 


104  PHOTOMETRICAL  MEASUREMENTS 

perchloride  of  gold.  The  time-rate  of  the  formation  of  a  finely 
divided  precipitate  of  gold  was  taken  as  a  function  of  the  lumi- 
nous intensity  of  the  light.  An  apparatus  based  on  such  prin- 
ciples would  be  an  actinometer  rather  than  a  photometer. 

THE   PHOTOMETER  BENCH 

96.  The  mounting  of  the  screen  and  its  containing  sight  box 
and  the  light  source,  varies  in  practice  according  to  individual 
requirements,  and  it  is  a  matter  that  may  be  left  to  the  design 
of  the  experimenter.     T^e  essential  for  the  proper  mounting  of 
the  photometrical  train  is  a  track  or  way  along  which  the  sight 
box  may  be  readily  moved  in  a  plane  parallel  with  the  pho- 
tometrical axis.     One  or  two  scales  should  be  provided;   an 
equably  divided  one  giving  the  distance  from  the  screen  to  each 
light  source ;  the  other  stating  the  setting  of  the  screen  directly 
in  light  units.      The  supports  for  the  light  standard  and  the 
compared  light  should  admit  of  ready  adjustment  of  the  height 
of  the  light  sources. 

Of  a  number  of  excellent  commercial  photometer  benches, 
perhaps  the  best  known  is  a  type  designed  in  connection  with 
the  investigations  at  the  Physikalische  Keichsanstalt. 

97.  The  Reichsanstalt  photometer  bench  is  commonly  made 
for  a  maximum  working  distance  between  the  light  sources  of 
either  200  or  250  centimetres.     The  sight  box  (Fig.  36),  sup- 
ports for  the  lights,  and  accessory  apparatus  are  mounted  on 
separate  carriages  which  may  be  readily  moved  or  adjusted 
along  a  track  or  clamped  in  a  desired  position.     The  track 
consists  of  two  hollow  steel   tubes   some  35  millimetres   in 
diameter,   and   separated  by  a  distance  of   12.5  centimetres 
between  their  centres.     The  rails  are  carried  by  two  cast-iron 
end  frames  and  a  central  or  stiffening  frame.     One,  and  in 
some  cases  two,  similar  tubes  are  placed  below  the  parallel  ones 
for  tie  rods.     This  construction  insures  a  stiff  and  at  the  same 
time  a  light  and  effective  mount.     The  frames  are  fitted  with 


PHOTOMETERS 


105 


106  PHOTOMETRICAL   MEASUREMENTS 

adjusting  screws  for  levelling  the  track.  The  experimenter 
may  work  from  either  side  'of  the  bench. 

The  entire  structure  should  be  coated  with  a  dull  black 
lacquer,  excepting  a  narrow  band  on  each  rail ;  this  is  silver 
plated  and  engraved  with  a  scale.  One  rod  carries  a  scale 
graduated  in  millimetres ;  the  other  one  may  have  engraved  on 
it  a  candle  power  or  other  light-unit  scale.  In  imported  benches 
the  candle  power  scale  is  based  on  the  German  candle.  Where 
the  carriage  wheels  bear  on  the  rails,  the  lacquer  will  soon  wear 
off,  exposing  a  reflecting  metallic  strip ;  an  attempted  remedy 
for  this  has  been  to  cover  the  rails  with  thin  hard  rubber  tubes. 

Each  carriage  rests  on  three  wheels  in  order  that  it  may 
adjust  itself  to  any  skewing  of  the  bench  or  inequalities  in  the 
rails.  The  carriage  is  fitted  with  a  clamp  which  grasps  the 
rail  between  the  wheel  and  a  curved  plate,  and  is  quickly 
applied  or  removed.  The  carriage  base  carries  a  socket  in 
which  slides  a  post  that  may  be  elevated  or  depressed  by  a 
rack  and  pinion,  and  also  clamped  at  any  height;  to  these 
posts  the  several  photometrical  members  of  the  train  are 
attached.  The  alignment  of  the  photometrical  train  is  easily 
accomplished,  and  the  lights  may  be  separated  to  any  desired 
distance  up  to  the  length  of  the  rails.*  The  bench  may  be 
mounted  on  pedestals  or  a  long  table,  and  this  should  be  so 
placed  in  the  room  as  to  permit  of  working  freely  on  either 
side. 

SPECTROPHOTOMETRY 

98.  In  the  discussion  of  the  Weber  photometer  (page  85)  a 
reference  was  made  to  the  measurement  of  a  light  source, 
viewing  the  field  successively  through  a  red  and  a  green  glass, 
and  combining  the  results  in  such  a  manner  that  the  total 
illuminating  effect  of  the  source  was  stated  as  a  function  of  the 

*  The  influence  of  the  working  distance  of  the  light  sources  on  the 
sensitiveness  of  the  settings  has  been  developed  by  Kriiss ;  Schilling's 
Journal,  1886,  page  890  ;  and  by  Strecker,  Elektrotech.  Zeitschrift,  1887, 
page  17. 


PHOTOMETERS  107 

measurements  obtained  with  these  two  screens.  This  method 
is  pregnant  with  suggestion  for  the  solution  of  some  of  the 
vexed  questions  in  the  photometrical  comparison  of  light 
sources,  and  the  illuminating  value  of  any  particular  source. 

The  extension  of  such  a  method  leads  to  a  class  of  measure- 
ments whose  object  is  the  comparison,  not  only  of  the  red  and 
green,  but  of  all  the  constituents  of  the  light  quality  by  means 
of  a  photometer,  which  shall  include  in  its  optical  train  some 
form  of  spectroscope.  The  necessary  apparatus,  however,  is 
complicated,  and  its  practice  belongs  rather  to  the  physical 
laboratory. 

Spectrophotometry  can  not,  in  its  present  development,  be 
considered  a  branch  of  applied  photometry,  though  it  may 
eventually  become  such  should  a  rational  standard  of  light 
quality  be  adopted  based  upon  its  physical  analysis.  The 
apparatus  and  methods  for  the  prosecution  of  spectropho- 
tometry  are  so  varied,  and  the  literature  of  the  subject 
is  so  extensive,  that  it  does  not  admit  of  treatment  in  this 
discussion. 

Briefly,  in  Spectrophotometry  a  spectrum  of  each  of  the  two 
light  sources  is  viewed,  the  one  appearing  located  above  the 
other  to  the  observer.  These  spectra  should  be  separated 
from  each  other  by  a  very  narrow  dark  band  with  sharply 
defined  limits,  and  they  are  adjusted  relatively,  so  that  corre- 
sponding colour  bands  or  wave  lengths  appear  one  over  the 
other.  The  act  of  measurement  then  consists  of  taking  the 
spectra,  colour  by  colour,  or  wave  length  by  wave  length,  and 
adjusting  either  the  distances  of  the  lights  or  the  position  of 
the  spectroscopic  sight  box,  as  the  case  may  be,  until  equal 
intensities  in  the  colour  groups  are  obtained.  If  this  is  done 
for  the  principal  colour  groups  of  each  spectrum,  not  only  will 
the  quality  of  each  light  source  be  known,  but  the  relative 
intensities  of  the  light  constituents. 

It  is  seldom  that  two  light  sources  will  show  identical 
quality ;  and  as  a  rule  they  differ  not  only  in  quality  or  colour 
constituents,  but  in  the  relative  intensity  of  these  constituents. 


108  PHOTOMETRICAL  MEASUREMENTS 

The  illuminating  power  of  any  light  source,  then,  is  defined 
between  these  two  variables,  and  a  truly  scientific  expression 
of  the  illuminating  power  would  follow  from  a  modification  of 
a  method  used  by  Maxwell.*  The  illuminating  power  of  each 
light  constituent  being  known,  the  total  illuminating  power  of 
the  light  source  would  be  a  function  determined  by  securing 
the  illuminating  powers  of  its  constituents.! 

*  Consult  Rood,  Text-book  of  Color,  pages  120  and  224. 

t  For  an  outline  of  the  apparatus  and  practice  of  spectrophotometry 
consult  Manual  of  Applied  Physics,  Nichols,  Vol.  II,  Chap.  IV.  For  an 
application  of  this  method  of  investigation  see  an  article  on  the  spectro- 
comparison  of  Auer  gas  mantles  with  arc  and  incandescent  lamps  by 
Mtitzel,  Electrotech.  Zeitschrift,  1894,  page  476. 


CHAPTER   IV 

STANDARDS   OF   ILLUMINATING   POWER 

99.    Illumination  distinguished  from  illuminating  power. — The 

ordinary  acts  of  vision  are  excited  through  light  which  is 
reflected  from  surfaces  into  the  eye.  This  gives  rise  prac- 
tically to  two  lines  of  investigation :  (1)  The  influence  of  the 
surface  upon  the  quality  of  the  light  falling  upon  it,  and  the 
percentage  of  the  whole  light  which  is  reflected  from  the  sur- 
face. Such  phenomena  come  within  the  scope  of  a  work  on 
illumination,  in  which,  however,  photometry  may  be  employed 
as  a  means  of  measurement.  And  (2)  the  character  and  in- 
tensity of  the  effect  which  a  source  of  light  exerts  directly  or 
indirectly  on  the  eye.  Photometry  deals  with  the  measure- 
ment of  these  effects.  These  two  classes  of  phenomena  are 
always  related  when  the  eye  is  excited  through  reflected 
light. 

In  general,  any  surface  from  which  the  eye  is  excited  to 
acts  of  vision  is  in  a  sense  a  light  source;  and  a  primary 
light  source  is  one  which  radiates  light  from  its  surface,  while 
a  secondary  light  source  reflects  the  light  from  its  surface. 

The  function  of  photometry,  then,  is  the  measurement  of  the 
illumination  from  reflecting  surfaces,  and  the  illuminating 
power  of  radiating  sources. 

It  is  obvious,  too,  that  the  illumination  from  reflecting  sur- 
faces is  ultimately  dependent  upon  the  illuminating  power  of 
light  sources,  and  that,  in  establishing  units  and  standards  for 
photometrical  measurements,  there  will  necessarily  be  certain 
fundamental  units  and  standards  of  illuminating  power, 

109 


110  PHOTOMETRICAL   MEASUREMENTS 

100.  Basis  for  photometrical  standards.  —  A  standard  of  illumi- 
nating power  is  not  primarily  a  physical  standard  of  light.     It 
was  emphasized  in  Chapter  I  that   photometrical   standards 
must  rest  primarily  on  a  physiological  basis.     Here  occurs  the 
confusion  in  many  discussions  of  these  subjects.     It  has  been 
advanced  that  standards  of  illuminating  power  are  not  possible, 
since  colour  and  light  sensations  are  not  stimulated  to  the  same 
degree  in  all  normal  eyes  by  sources  of  the  same  intensity  and 
quality,  even  though  all  such  eyes  perfectly  agree  in  the  power 
to  discriminate  colours  and  colour  shades.*     This  consideration 
is  not  only  confusing,  but  foreign  to  the  subject  of  standards  of 
illuminating  power,  for  experimental  data  show  that  different 
normal  eyes  vary  in  the  intensity  rather  than  the  quality  of 
their  sight  sensations.     As  a  consequence  of  Fechner's  law,  it 
is  not  the  magnitude  of  the  sight  sensation  which  is  to  be  meas- 
ured in  photometry,  but  the  magnitude  of  the  stimulation. 

The  true  basis  for  standards  of  illuminating  power  was 
indicated  in  Chapter  I.  This  basis  was  found  to  be  empirical, 
and  its  character  was  defined  by  the  investigations  of  Young, 
Helmholtz,  Maxwell,  and  others. 

101.  A  fundamental  standard  of  illuminating  power  impossible. f 
—  In  order  to  reduce  the  physical  properties  of  ether  waves  of 
any  frequency  to  a  fundamental  standard  expressed  in  centi- 
metre-gram me-second  measure,  it  is  necessary  to  establish  for 
them  an  invariably  constant  and  measurable  effect.     But  such 
an  effect  must   be   purely  physical  in  order  to  be   constant, 
as  the  heating  effect  on  a  blackened  surface.     When  it  has 
to  deal  with  the  illuminating  power  of  ether  waves,  the  eye, 
in  a  sense,  behaves  toward  them  like  a  galvanometer  toward 
the  electric  current.     But  the  eye,  as  a  metering  instrument 
for   light,  does  not  give  an  unvarying  result  for   the   same 
amount  and  character  of  stimulation,  as  was  pointed  out  in  the 

*  Compare  a  suggestion  by  Abney,  British  Association  Report ;  1883, 
page  424. 

t  Consult  Blondel,  "The  Continuous  Current  Arc,"  Proceedings  Inter- 
national Electrical  Congress  ;  1893,  pages  316-317, 


STANDARDS   OF   ILLUMINATING  POWER  111 

discussion  of  Fechner's  law  (page  15).  An  empirical,  and  to 
some  extent  arbitrary,  standard  only  is  possible,  and  when  this 
is  once  adopted  and  defined,  it  can  be  ultimately  reduced  to 
fundamental  centimetre-gramme-second  measure  of  heat  waves ; 
but  this  will  in  no  sense  define  the  illuminating  power. 

102.  The  ideal  photometrical  standard.  —  The  mechanism  of 
the  various  photometrical  screens  and  benches  has  reached  a 
high  state  of  accuracy  and  perfection,  and  far  excels  in  these 
respects  all  known  standards  of  illuminating  power.  The 
errors  and  uncertainties  in  photometrical  measurements  origi- 
nate in  nearly  all  cases  from  unsatisfactory  light  standards. 
Probably  no  one  subject  in  physical  measurements  has  received 
more  painstaking  investigation,  but  the  results  so  far  obtained 
are  all  far  from  satisfactory  in  their  ability  to  establish  a 
standard  of  illuminating  power.  The  importance  is  then 
apparent  of  an  attempt  to  obtain  a  clear  conception  of  the 
properties  of  an  ideal  standard  in  photometry. 

A  satisfactory  empirical  standard  must  emit  ether  waves  of 
such  frequencies  and  intensities  as  shall  excite  the  primary 
colour  sensations  of  red,  green,  and  violet,  as  indicated  by  data 
obtained  from  experiments.  The  curves  given  by  Helmholtz 
and  confirmed  by  Maxwell  (Fig.  4,  page  14)  may  be  accepted  as 
rational  until  further  investigation  shall  indicate  their  improve- 
ment. The  ideal  standard,  then,  would  conform  to  these  curves, 
and  its  conformity  could  be  accurately  measured  by  means  of 
the  spectrum  photometer. 

None  of  the  photometrical  standards  now  in  general  use  con- 
forms to  these  requirements.  As  a  rule,  each  unduly  empha- 
sizes either  the  red  or  violet  colour  group.  Carbon,  heated 
to  a  certain  high  temperature,  appears  to  fulfil  these  condi- 
tions with  satisfactory  exactness,  as  in  an  incandescent  lamp 
exhausted  until  the  blue  glow  disappears.  As  yet  this  par- 
ticular temperature  has  not  been  exactly  determined.  The 
acetylene  gas  flame,  on  account  of  the  whiteness  of  its  light, 
also  promises  well  as  a  standard  flame. 


112  PHOTOMETKICAL  MEASUREMENTS 

103.  Requirements  for  the  photometrical  standard.  —  In  addi- 
tion to  the  optical  properties  just  considered,  a  practical  stand- 
ard should  fulfil  the  conditions  :  — 

1.  Simplicity  of  construction  and  operation. 

2.  Reasonable  permanence  of  its  parts. 

3.  Reproducibility  with  accuracy. 

4.  Constancy  in  operation. 

104.  The  practical  unit  of  illuminating  power.  —  There  is  no 
generally  accepted  national  or  international  unit  of  illuminating 
power.     In  the  United  States  and  in  England  the  prevailing 
unit  is  the  candle  power  based  on  the  spermaceti  candle ;  in 
Germany  another  candle-power  unit  is  in  general  use,  but  this 
is  based  on  the    paraffine    candle  (Vereinskerze) ;    while   in 
France  the  accepted  unit  is  the  carcel,  based  on  a  peculiar 
argand  lamp  of  that  name. 

The  photometrical  unit  must  eventually  be  arbitrarily  chosen, 
and  may  or  may  not  be  the  value  of  the  standard  of  illuminat- 
ing power.  Though  as  the  standards  more  nearly  approach 
the  theoretical  requirements,  it  is  obviously  absurd  to  continue 
to  evaluate  them  in  terms  of  an  imperfect  unit  such  as  the 
carcel,  or  candle  power,  especially  since  by  all  rules  of  enumer- 
ation the  unit  should  be  of  the  same  character  as  the  standard. 

105.  The  luminosity  of  flames. — This  subject  is  one  which 
presents   many  difficulties   and   obscurities,  and  though  fre- 
quently investigated,  the  results  obtained  are  widely  divergent. 

For  the  purposes  of  photometry  a  general  outline  of  flame 
phenomena  may  be  given.  When  the  combustible  is  either 
solid  or  liquid,  a  wick  is  employed  to  feed  it  to  the  flame.  The 
liquid  combustible  —  for  if  a  solid,  it  is  melted  by  the  heat  of 
the  flame  —  passes  through  the  wick  by  capillary  action  at  a 
rate  determined  by  the  physical  conditions  which  influence 
the  capillary  action.  Gaseous  combustibles  are  supplied  to  the 
flame  under  regulated  pressure  through  an  opening  in  a  tube. 
The  combustible  in  any  case  consists  chiefly  of  hydrocarbons, 


STANDARDS    OF    ILLUMINATING   POWER  113 

compounds  of  carbon  and  hydrogen,  singly  or  in  combination 
with  compounds  of  carbon,  hydrogen,  and  oxygen. 

A  flame  consists  of  three  principal  cones  or  layers.  In  the 
inner  one  the  combustible  is  heated  and  undergoes  decompo- 
sition, and  no  light  is  emitted  from  it.  In  the  central  layer 
carbon  and  very  dense  hydrocarbons  are  liberated,  which  being 
heated  to  incandescence  constitute  the  principal  source  of 
luminosity.  In  the  outer  layer  the  oxidation  of  the  carbon  and 
hydrogen  is  completed,  and  this  layer  feebly  contributes  to  the 
light  emitted  by  the  flame  by  means  of  incandescent  gases  and 
vapors.  A  flame,  briefly,  is  the  seat  of  exceedingly  complicated 
chemical  reactions  delicately  balanced  and  subject  to  sudden 
and  marked  variations,  and  is  as  well  the  focus  of  streams  of 
cooling  and  diluting  gases  from  the  surrounding  air.  * 

106,  The  influence  of  variations  of  atmospheric  pressure  on  the 
luminosity  of  flames.  —  In  1859  Frankland  and  Tyndall  made 
some  interesting  experiments  to  determine  the  influence  of  high 
elevation  on  the  rate  of  consumption  of  the  combustible,  and 
the  luminosity  of  the  flame,  t  They  found  the  amount  of  com- 
bustible consumed  per  hour  was  practically  unaffected  by  the 
pressure  of  the  air,  and  with  the  low  atmospheric  pressure 
which  occurs  at  the  top  of  Mt.  Blanc  the  candle  flame  became 
as  non-luminous  as  that  of  the  Bunsen  burner. 

Frankland  subsequently  extended  these  investigations  and 
found,  in  general,  that  on  decreasing  the  air  pressure  even  a 
smoky  flame  burns  clearly,  and  tends  toward  the  low  luminosity 
of  the  Bunsen  burner;  while  by  increase  of  pressure  an  alco- 
holic flame,  too,  becomes  white  and  luminous.  Frankland  con- 
cluded that  "the  variations  of  illuminating  power  depend 
chiefly,  if  not  entirely,  upon  the  ready  access  or  comparative 
exclusion  of  atmospheric  oxygen  as  regards  the  interior  of  the 

*  An  interesting  discussion  of  the  luminosity  of  flames  was  given  by 
Professor  Vivian  Lewes  in  his  London  Institution  lectures.  Consult  the 
Scientific  American  Supplement,  April  2,  1892,  page  13,544. 

t  Heat  as  a  Mode  of  Motion,  Tyndall,  page  64. 

i 


114  PHOTOMETRIC AL   MEASUREMENTS 

flame."*  With,  decrease  of  pressure  the  flame  became  more 
permeable  to  the  surrounding  air,  and  the  combustible  being 
more  completely  oxidized  and  diluted,  the  flame  -correspond- 
ingly decreased  in  luminosity. 

107.  The  influence  of  the  height  of  the  flame  on  the  illuminating 
power.  —  This  aspect  of  the  investigation  of  light  standards  has 
received  marked  attention,  f  and  the  data  are  both  voluminous 
and  widely  divergent.      Whatever  may  be  the  gas-producing 
power  of  a  combustible,  either  solid  or  liquid,  there  is  a  critical 
flame  height  which  may  be  taken  as  a  normal  one  for  that 
illuminant,  and  it  is  seemingly  influenced  by  the  rate  at  which 
the  atmospheric  oxygen  penetrates  the  flame.     A  flame  increas- 
ing toward  the  normal  height  grows  hotter  and  the  decompo- 
sition of  the  combustible  is  more  active.     When  the  normal 
height  is  exceeded,  the  incomplete  supply  of  oxygen  produces 
rapid  lengthening  of  the  flame.     The  changes  of  flame  length 
would  then  be  greater  both  below  and  above  the  normal  height. 

It  has  also  been  established  for  practically  all  flames,  that 
the  illuminating  power  varies  proportionally  with  the  flame 
height  for  limits  of  at  least  ±  5  per  cent  on  either  side  of  the 
normal  height. 

1 08 .  The  effect  of  moisture  on  the  luminosity  of  flames  —  When 
a  chemically  inert  gas  or  vapour  is  introduced  into  a  luminous 
flame,   there   generally   results   a   marked   diminution   of  its 
illuminating  power,  though  experiments  have  not  so  far  shown 
conclusively  in  what  manner  the  diluting  substance  affects  the 
flame,  other  than  to  reduce  and  alter  the  light  emitted.     In  this 
way  non-combustible  constituents  of  the  atmosphere,  such  as 
aqueous  vapour  and  carbon  dioxide,  may  be  expected  to  influence 
the  light  values  of  all  flames ;  and  as  the  proportions  of  these 
substances  vary  so  greatly  from  time  to  time,  they  must  intro- 
duce error  and  uncertainty  in  flame  measurements. 

*  Philosophical  Transactions  ;  1861,  page  652. 

t  Probably  the  most  thorough  investigation  has  been  made  by  Hugo 
Kriiss,  Schilling's  Journal,  1883,  page  511. 


STANDARDS   OF   ILLUMINATING   POWER  115 


THE  ENGLISH  CANDLE 

109.  A  committee  of  the  British  Association  reporting  in  1888 
on  light  standards*  stated,  "The  present  standard  candle  is' 
not  worthy  in  the  present  state  of  science  of  being  called  a 
standard."     In  detail  its  faults  were  specified  to  be  uncertainty 
in  the  composition  of  the  spermaceti  and  the  weaving  of  the 
wick ;  the  fluctuations  in  the  flame  from  the  variations  in  the 
length  and  form  of  the  wick  while  burning,  and  the  filling  and 
emptying  of  the  cup  of  the  candle.     These  conclusions  were 
based  on  an  extended  series  of  measurements  performed  with 
unusual  accuracy  and  care. 

The  untrustworthiness  of  the  candle  to  serve  as  a  standard 
of  light  has  been  recognized  from  the  earliest  practice  of  pho- 
tometry. Various  investigators  have  examined  it  with  more  or 
less  thoroughness,  and  always  with  the  result  so  clearly  and 
authoritatively  expressed  in  this  report  of  the  Committee  of 
the  British  Association. 

110.  The  character  of  the  light.  —  Aside  from  all  considerations 
of  the  constancy  of  the  illuminating  power  of  the  candle,  the 
quality  of  its  light  would  render  it  unsatisfactory  as  a  standard. 
Candle  light  does  not  excite  the  eye  normally ;  the  light  is  too 
red,  and  is  deficient  both  in  the  extent  and  relative  intensity  of 
the  violet  colour  group.     In  consequence,  it  is  unable  to  bring 
out  the  full  values  of  colours  in  which  greenish  blue,  blue,  or  vio- 
let shades  are  constituents.     Under  the  ordinary  conditions  of 
burning,  the  character  of  the  flame  does  not  permit  sufficiently 
high  incandescence  of  the  free  carbon  contained  in  it  to  emit, 
in  normal  proportions,  those  wave  frequencies  belonging  to  the 
violet  colour  group. 

*  Proceedings  British  Association,  1888,  page  39  (Reports).  For  a 
clear  statement  of  the  events  in  the  burning  of  a  candle,  consult  "The 
Chemical  History  of  a  Candle,"  by  Faraday,  especially  Lectures  I 
and  II. 


116  PHOTOMETRICAL  MEASUREMENTS 

111.  Description  and  specifications.*  —  The  finished  candle  is 
ten  inches  long,  and  is  0.9  inch  in  diameter  at  the  bottom,  and 
tapers  slightly  to  0.8  inch  diameter  at  the  top.  The  wick 
should  be  made  of  three  strands  of  cotton  plaited  together,  each 
strand  consisting  of  eighteen  threads.  The  strands  should  be 
plaited  with  such  closeness  that,  when  the  wick  is  laid  upon  a 
rule  and  extended  by  a  pull  just  sufficient  to  straighten  it,  the 
number  of  plaits  in  four  inches  should  not  exceed  thirty -four 
nor  be  less  than  thirty -two. 

The  wicks  should  be  steeped  in  a  liquid  made  by  dissolving 
one  ounce  of  crystallized  boracic  acid  in  a  gallon  of  distilled 
water  to  which  two  ounces  of  liquid  ammonia  have  been  added. 
The  wicks  are  then  to  be  pressed  until  most  of  the  liquid  has 
been  removed,  and  dried  at  a  moderate  heat.  Twelve  inches  of 
the  wick  thus  made  should  not  weigh  more  than  6.5  nor  less 
than  six  grains.  The  weight  of  the  ash  remaining  after  the 
burning  of  ten  wicks  which  have  not  been  steeped  in  boracic 
acid,  or  from  which  the  boracic  acid  has  been  removed  by 
washing,  should  not  be  more  than  0.025  grain. 

The  spermaceti  of  which  the  candles  are  made  should  be 
extracted  from  crude  sperm  oil,  and  it  should  be  so  refined  that 
it  has  a  melting  point*  lying  between  112°  and  115°  Fahr. 
Since  the  candles  made  with  spermaceti  alone  are  brittle,  and 
the  cup  which  they  form  in  burning  has  an  uneven  edge,  it  is 
necessary  to  add  a  small  portion  of  beeswax  or  paraffine  to 
remedy  these  defects.  The  best  air-bleached  beeswax  melting 
at  about  144°  Fahr.  is  to  be  added  to  the  spermaceti  in  pro- 
portions of  not  less  than  three  per  cent  and  not  more  than  4.5 
per  cent. 

The  candles  made  with  the  materials  above  described  should 
weigh,  as  nearly  as  may  be,  one-sixth  of  a  pound.  As  the  rate  of 
burning  of  a  candle  is  affected  by  the  force  with  which  the  wick 
is  pulled  when  it  is  set  in  the  mould,  the  strain  commonly  applied 
by  the  careful  maker  is  found  to  be  about  twenty-four  ounces. 

*The  full  text  of  the  specifications  issued  by  the  Metropolitan  Gas 
Referees  may  be  found  in  American  Gas  Light  Journal ;  60, 1894,  page  41. 


STANDARDS   OF  ILLUMINATING  POWER  117 

The  wicks,  before  steeping,  should  be  washed,  first  in  dis- 
tilled water  made  alkaline  with  one  or  two  per  cent  of  strong 
liquid  ammonia,  then  in  a  ten  per  cent  solution  of  nitric  acid; 
and  finally  should  be  thoroughly  and  repeatedly  washed  in 
distilled  water. 

112.  The  influence  of  the  state  of  the  combustible.*  —  The  com- 
position of  the  wax  of  the  sperm  candle  is  always  more  or  less 
uncertain.     Owing  to  difficulties  in  separating  the  spermaceti 
from  the  sperm  oil  of  which  in  the  crude  state  it  is  a  constit- 
uent, the  solid  spermaceti  invariably  contains  more  or  less  oil 
whose  effect  is  to  increase  the  luminosity  of  the  candle  flame. 
As  the  processes  for  the  separation  of  the  spermaceti  have 
improved,  the  wax  has  become  "  drier,"  and  the  luminosity  of 
the  standard  candle  has  been  observed  to  decrease  proportion- 
ately.     Another  element  of  uncertainty  is  introduced  in  the 
small  amount  of  beeswax  which  is  added  to  the  spermaceti  to 
overcome  its  tendency  to  crystallize. 

113.  The  influence  of  the  wick.  —  The  exposed  portion  of  the 
wick,  as  it  increases  in  length  when  the  candle  is  burning, 
usually  becomes  curved  and  deforms  the  flame,  especially  at 
its  base.    Methven  f  found  a  maximum  change  in  candle  power 
from  this  cause  alone  of  four  per  cent;   and  that  the  best 
average  candle  power  was  obtained  when  the  plane  of  the 
curvature  of  the  wick  was  at  right  angles  to  the  plane  of  the 
screen,  the  wick  being  curved  from  the  screen.     As  the  wick 
curves,  it  deforms  the  flame,  and  by  displacing  the  centre  of 
the  light  source,  has  the  effect  of  changing  the  length  of  the 
photometer  bar.      The   charring   of  the  wick   influences   the 
capillary  flow  of  the  melted  wax  to  the  flame,  and  this  disturb- 
ance is  not  without  its  effect  on  the  candle  power  of  the  flame. 
The  wick  is  usually  treated  in  a  dilute  solution  of  an  alkaline 

*  Consult  "Soaps  and  Candles,"  W.  L.  Carpenter,  Chapter  XII,  and 
especially  page  240. 

t  London  Gas  World,  Nov.  30,  1889,  page  597. 


118  PHOTOMETRICAL   MEASUREMENTS 

borate,  or  similar  substance,  to  cause  a  fusion  of  the  ash. 
Besides  modifying  the  action  of  the  wick  such  substances 
impart  a  slightly  greenish  yellow  tinge  to  the  flame.* 

The  size  of  the  wick  is  of  significance,  governing,  as  it  does, 
the  amount  of  the  combustible  consumed.  It  is  so  designed  in 
thickness  and  weave  that  it  will  supply  120  grains  per  hour 
under  the  ordinary  conditions  of  burning. 

The  height  of  the  flame  is  dependent  on  the  length  of  the 
wick  above  the  melted  wax  in  the  cup.  With  a  flame  burning 
uniformly  and  undisturbed,  the  cup  will  form  with  an  even  rim 
and  the  melted  wax  will  not  escape.  But  should  the  side  of 
the  cup  be  melted  down  and  the  contents  escape,  the  length 
of  the  exposed  wick  is  considerably  increased. 

114.  The  normal  flame  height.  —  This  is  now  accepted  to  be  45 
millimetres,  and  it  is  practically  necessary  to  take  the  measure- 
ments of  candle  power  at  this  particular  height,  for  only  very 
approximate  corrections  can  be  applied.     When  this  height  is 
exceeded,  the  wick  must  be  snuffed,  and  in  order  that  the  flame 
may  be  steady  at  the  normal  height  for  even  a  short  time,  the 
snuffing  of  the  wick  must  be  done  with  care,  and  frequently 
repeated,  removing  but  a  little  at  a  time. 

The  measurement  of  the  flame  height  is  rendered  difficult 
through  the  rapid  movements  at  the  base  of  the  flame,  and  the 
feeble  luminosity  of  this  portion.  The  height  may  be  observed 
by  means  of  a  suitable  cathetometer  or  a  reading  telescope  and 
a  vertical  scale  f  placed  close  to  the  flame ;  or  an  image  of  the 
flame  may  be  projected  on  a  screen  and  directly  measured. 

115.  The  influence  of  air  currents.  —  All   open  flames  are 
extremely  sensitive  to  disturbances  in  the  air  about  them ; 

*  Other  specifications  require  the  wick  to  be  thoroughly  washed  in 
distilled  water,  then  treated  with  a  1  to  2  per  cent  solution  of  ammonium 
hydrate,  followed  by  immersion  in  a  ten  per  cent  solution  of  sulphuric  acid, 
and  a  final  washing  in  distilled  water. 

t  Hugo  Kriiss,  Schilling's  Journal,  1883,  page  717,  describes  a  compact 
instrument  of  this  character  for  measuring  flame  height. 


STANDARDS   OF   ILLUMINATING  POWER  119 

and  while  urging  objections  of  such  a  nature  against  the  candle, 
it  must  be  granted  that  the  effects  of  mechanical  disturbances 
on  the  flame  itself  are  the  same  for  all  unprotected  flames. 
Even  a  slight  movement  of  the  arm  while  adjusting  the  screen 
may  cause  the  open  flame  to  waver. 

One  of  the  greatest  difficulties  in  the  use  of  the  candle  is  to 
maintain  a  steady  flame ;  and  such  flames  are  practically  suit- 
able for  measurement  only  during  short  and  infrequent  inter- 
vals, for  the  air  of  a  room  is  continually  disturbed  by  currents 
caused  by  the  unequal  temperature  of  the  walls  and  floor, 
drafts,  and  the  convection  currents  set  up  by  the  flame  itself. 

If  a  candle  flame  is  blown  to  one  side  by  a  draft,  heated  air 
is  directed  against  the  walls  of  the  cup,  and  they  are  apt  to 
yield  and  allow  the  melted  wax  to  flow  out.  This  lengthens 
the  wick,  with  a  corresponding  increase  in  flame  height.  An 
inopportune  draft,  when  all  conditions  for  reading  the  screen 
are  normal,  may  lose  the  reading  to  the  observer  and  necessitate 
a  renewed  trimming  of  the  wick,  and  a  repetition  of  bringing  the 
standard  up  to  normal  conditions.  A  draft  will  also  change 
the  balance  of  the  chemical  reactions  in  the  flame,  by  affecting 
the  decomposition  and  the  rate  of  oxidation  of  the  combustible. 

There  is  no  efficient  protection  for  open  flames  against  air 
currents.  When  a  candle  flame,  for  instance,  is  enclosed  in  a 
box,  unless  it  is  a  very  wide  one,  it  will  induce  drafts,  and 
these,  by  increasing  the  oxidation-rate  of  the  flame,  will  reduce 
the  luminosity.  The  same  action  is  greatly  intensified  by  the 
use  of  a  chimney. 

116.  The  influence  of  moisture  in  the  air.  —  The  degree  of 
humidity  of  the  atmosphere  in  which  a  candle  is  burned  pro- 
portionately reduces  its  illuminating  power.  Methven  *  found 
with  a  constant  weight  of  candle  burned,  120  grains  per  hour, 
that  the  luminosity  decreased  as  much  as  8.4  per  cent  due  to 
moisture  in  the  air.  A  candle  consuming  120  grains  in  one 
hour  in  dry  air  gave  1.196  units,  and  while  burning  in  moist 

*  London  Gas  World,  Nov.  30,  1899,  page  598. 


120  PHOTOMETRICAL   MEASUREMENTS 

air  under  the  same  conditions  of  flame  height  and  consumption 
it  gave  only  1.104  units  of  illuminating  power. 

117.  The  influence  of  air  pressure.  —  Though  Frankland  has 
shown  the  general  influence  of  the  variation  in  air  pressure  on 
the  luminosity  of  the  candle  flame  (page  113),  more  exact 
determinations  are  not  necessary.     At  any  given  pressure  the 
variations  in  the  illuminating  power  of  the  candle  are  so  great 
and  uncertain  that  it  is  unnecessary  to  attempt  to  introduce  a 
correction  for  changes  in  the  atmospheric  pressure. 

118.  The  time  variations  of  the  flame.  —  Summing  up  the  many 
causes  of  variation  in  the  illuminating  power  of  the  candle 
flame,  it  is  evident  that  the  fluctuations  will  not  only  be  large 
in  amount,  but  will  occur  rapidly.     Were  such  a  flame,  even 
under  a  certain  set  of  conditions,  suitable  for  a  light  standard, 
these  would  change  so  quickly  that  its  value  as  a  standard 
would  be  seriously  impaired.    All  this  may  be  made  evident  by 
watching  a  candle  burning  in  a  darkened  room.     Some  pains- 
taking experiments  have  been  carried  out  in  an  endeavour  to 
show  these  changes  graphically.* 

119.  Requirements  for  unit  candle  power.f  —  The  spermaceti 
candle  is  supposed  to  emit  unit  illumination  when  consuming 
120  grains  of  combustible  per  hour,  at  a  flame  height  of  45 
millimetres,  while  burning  in  dry  air  under  normal  atmospheric 
pressure. 

120.  Directions  for  the  use  of  a  standard  candle.  —  In  the  course 
of  this  discussion  of  the  English  candle  many  considerations 
have  been  established  which  point  to  the  non-use  of  the  candle 

*  Physical  Review,  Vol.  II,  page  1 ;  also  Transactions  American  Insti- 
tute of  Electrical  Engineers,  1896,  pages  133-205.  These  methods  are 
based  on  the  supposition  that  the  heat  radiated  from  a  flame  and  the  illu- 
mination it  emits  are  in  a  constant  ratio  ;  a  proposition  of  no  real  photo- 
metrical  value. 

t  For  recent  specifications  for  the  English  candle,  consult  an  article  by 
E.  G.  Love,  in  the  American  Gas  Light  Journal,  March  5, 1894,  page  326. 


STANDARDS   OF   ILLUMINATING  POWER  121 

as  a  light  unit  for  photometry.  The  references  given  are 
deemed  sufficient  for  the  needs  of  investigators,  yet  it  may 
be  desirable  to  recapitulate  briefly  such  directions  as  should 
be  observed  when  the  candle  is  used.  The  candle  should  be 
allowed  to  burn  for  at  least  fifteen  minutes  before  taking  any 
measurements  with  it.  The  flame  should  not  be  enclosed  in 
either  box  or  chimney.  Finally,  when  the  top  of  the  candle  is 
well  cupped,  the  wick  is  trimmed,  and  the  flame  length  observed 
as  it  increases,  and  when  this  is  45  millimetres,  the  position  of 
the  screen  is  read.  The  disturbing  conditions  and  the  pre- 
cautions to  be  taken  in  connection  with  these  must  be  carefully 
observed. 

THE   GERMAN   CANDLE    (VEREINS  NORMALKERZE) 

121.  Description. — This  light  standard  was  adopted  in  1869, 
and  definitely  specified  by  a  Commission  of  the  Gas  and  Water 
Works  Association  of  Germany  in  1871.*  These  specifications 
were  unusually  minute,  and  applied  to  the  material  and 
methods  of  manufacture,  and  directions  for  the  use  of  the 
standard. f  In  order  to  insure  uniformity  in  their  manufacture, 
the  candles  are  made  under  the  supervision  of  a  commission  of 
the  association,  and  are  supplied  by  the  association  under  a 
guarantee  that  they  fulfil  the  specifications  for  the  combus- 
tible, the  wick,  and  the  size  and  weight  of  the  finished  candle. 
It  is  accordingly  named  the  Vereinskerze. 

The  specifications  require  a  twisted  wick  of  25  cotton 
threads,  one  metre  of  the  finished  wick  weighing  668  milli- 
grammes. The  candle  has  a  uniform  diameter  of  20  millimetres, 
and  when  of  the  standard  length  of  314  millimetres  should 
weigh  83.6  grammes.  The  same  elaborate  attention  is  paid  to 
cleansing  the  wick  as  in  the  manufacture  of  the  English  candle. 

*  Schilling's  Journal,  1869,  pages  364  and  521,  and  succeeding  reports 
of  the  Commission  for  Light  Measurements. 

t  The  full  text  of  the  specifications  is  given  in  Schilling's  Journal,  1871, 
page  684. 


122  PHOTOMETRICAL   MEASUREMENTS 

122.  The  combustible  is  paraffine  which  has  been  highly  puri- 
fied.    To  fulfil  the  specifications,  it  should  have  a  melting 
point  of  55°  Centigrade.     The  paraffine  of  commerce  is  a  mix- 
ture of  a  number  of  members  of  the  paraffine  series  whose 
chemical   constitution   corresponds    to    the    general    formula, 
CMH2n+2. 

The  properties  of  the  successive  members  of  this  series  are 
so  similar  that  it  is  difficult  to  obtain  the  substance  called 
paraffine  wax  having  an  invariable  composition.  By  an  ad- 
mixture of  paraffine  oil,  vaseline,  and  paraffine  wax  in  varying 
proportions,  it  is  possible  to  maintain  the  melting  point  of 
the  mixture  at  a  determinate  temperature,  while  the  chemical 
character  of  the  mixture  may  show  wide  variations. 

Paraffine  wax*  being  a  mixture  of  indeterminate  composition, 
is  for  this  reason  alone  unsuited  to  serve  as  the  combustible  in 
a  standard  of  illuminating  power. 

123.  The  wick  essentially  resembles  in  its  character  that  used 
in  the  English  candle  (page  116),  with  the  exception  of  its  size, 
as  indicated  on  page  121 ;  and  it  received  from  the  Commission 
the  most  careful  attention  in  all  details  relating  to  the  quality 
and  cleansing  of  the  cotton,  the  size  and  weaving  tension  of  the 
strands,  and  even  the  tension  of  the  wick  in  the  mould. 

124.  The  colour  of  the  flame  and  the  normal  flame  height. — 

The  flame  is  slightly  whiter  than  that  of  the  spermaceti  candle, 
but  it  is  liable  to  smoke  and  to  split  into  a  number  of  points 
near  the  top. 

The  German  paraffine  candle  is  supposed  to  emit  unit  light 
strength  when  burning  with  a  clean  wick  and  a  flame  height 
of  50  millimetres.  The  quantity  of  combustible  consumed  an 
hour  is  not  found  to  be  significant,  and  is  not  prescribed  in  the 
definition  of  the  standard  candle. 

*  For  a  discussion  of  the  manufacture  of  paraffine,  and  its  physical 
properties,  consult  "Petroleum,"  by  Boverton  Redwood,  1894;  especially 
Vol.  I,  page  214. 


STANDARDS    OF   ILLUMINATING   POWER  123 

125.  The  behaviour  of  the  paraffine  candle  is  generally  similar 
to  that  of  the  spermaceti  candle,  and  all  the  conclusions  estab- 
lished for  the  latter  are  equally  applicable  to  both  varieties  of 
these  light  standards. 

Manufactured  under  the  conditions  described,  the  candles  of 
the  German  Commission  have  reached  a  high  state  of  perfec- 
tion as  a  product,  but  owing  to  inherent  objections  to  the  use 
of  any  form  of  candle  for  a  standard  of  illuminating  power, 
the  use  of  the  paraffine  candle  has  been  largely  abandoned  in 
Germany  and  elsewhere. 

In  addition  to  the  English  candle  and  the  Vereinskerze, 
there  are  a  number  of  less  widely  used  standard  candles, 
amongst  which  are  the  Star  and  Munich  candles.  These  differ 
in  no  essential  matters  from  the  forms  already  discussed. 

THE  CARCEL   LAMP 

126.  The  central  draft  type  of  burner,  known  as  the  argand, 
and  burning  vegetable  or  mineral  oil,  furnishes  a  source  of 
light,  not  only  of  remarkable  steadiness  of  flame,  but  owing  to 
the  introduction  of  the  air  within  the  flame,  of  marked  white- 
ness of  colour,  compared  with  similar  flames  burning  in  the 
ordinary  manner.     The  argand  type,  having  been  greatly  im- 
proved in  1802  by  Carcel,*  subsequently  attained  great  favour 
in  France  as  a  light  standard.     Its  properties  were  carefully 
investigated  by  Audoin  and  Bevard,  working  under  the  super- 
vision of  Dumas  and  Regnault.f     Through  the  labours  of  these 
investigators  its  constants  and  dimensions  were  defined.  $ 

The  carcel  lamp,  until  quite  recently,  has  been  the  light 
standard  generally  recognized  and  used  in  France,  where  the 
illuminating  power  of  light  sources  has  invariably  been 

*  By  the  improvement  added  to  the  argand  lamp  by  Carcel  and  Careau, 
the  oil  was  supplied  to  the  wick  at  a  uniform  rate  by  a  pump  operated  by 
clock-work.  Nicholson's  Journal,  II,  1802,  page  108. 

t  Annales  de  Chimie  et  de  Physique,  (3)  tome  Ixv,  page  423. 

J  Ref.  cit,  page  489. 


124  PHOTOMETRIC AL  MEASUREMENTS 

expressed  in  terms  of  the  carcel  unit.  Though  frequently 
investigated  in  other  countries,*  it  has  not  been  favourably 
received,  and  it  probably  should  not  be  classed  as  an  interna- 
tional light  standard. 

127.  The   essential  dimensions  of  the  lamp,   as   denned  by 
Dumas  and  Regnault  for  the  Paris  Gas  Association,  are  given 
below  and  illustrated  in  the  sectional  drawing  of  the  burner 
and  chimney  shown  in  Fignre  37. 

Greater  diameter  of  the  wick  tube         .         .         .  23.5  millimetres 

Internal  diameter  of  the  air  duct           ...  17  " 

Height  of  the  glass  chimney          .        .        .        .  290  " 

Internal  diameter  of  the  chimney  at  top        .  34  " 

Internal  diameter  of  the  chimney  at  base      .         .  47  " 

Mean  thickness  of  the  glass            ....  2  " 

Height  of  the  chimney  to  the  bend                         •.  61  " 

The  dimensions  of  the  metallic  parts  of  this  standard  may 
be  reproduced  with  sufficient  accuracy,  but  those  relating  to 
the  glass  chimney,  the  mean  thickness  of  the  wall,  and  the 
position  and  curvature  of  the  bend,  are  from  the  character  of 
the  manufacture  of  the  envelope,  not  capable  of  sufficiently 
exact  reproduction. 

128.  The  combustible  generally  employed  in  the  lamp  has  been 
colza-oil  (rape-seed  oil).     Such  a  vegetable  oil  is  not  a  suf- 
ficiently simple  and  definite  chemical  compound  to  satisfy  the 
requirements   for  the   combustible   for   a  light  standard.     It 
varies  considerably,  according  to  the  processes  followed  in  its 
preparation,  and  is  not  obtained  in  a  state  of  definite  purity. 
Attempts  have  been  made  to  burn  kerosene  in  the  carcel  lamp, 
but  no  more  constant  results  were  obtained. 

Dumas  and  Regnault  found,  with  a  consumption  of  42 
grammes  of  colza-oil  an  hour,  that  they  obtained  the  least 

*  Consult  a  paper  by  Thomas  N.  Kirkham  on  Tests  of  Candles  and  the 
Carcel  Lamp,  and  also  the  accompanying  discussion.  Proceedings  In- 
stitute of  Civil  Engineers  j  23,  1869,  page  447. 


STANDARDS   OF   ILLUMINATING  POWER 


125 


-34 » 


variation  of  illuminating  power  for  a  given  variation  in  the 

weight  of  the  combustible  consumed.     Accordingly  the  carcel 

lamp  is  supposed  to  furnish  standard  illuminating  power  when 

the   oil   consumption    is    42 

grammes  an  hour,  the  lamp 

being  operated  on  a  suitable 

balance   for    indicating    the 

rate    at    which    the    oil    is 

burned. 


129.  The  wick  is  a  matter 
of  considerable  importance 
in  such  a  lamp,  the  illumi- 
nating power  varying  to  a 
marked  degree  according  as 
a  fine,  medium,  or  coarse 
wick  is  used.*  The  standard 
wick  is  one  of  medium  mesh, 
and  consists  of  75  threads, 
and  weighs  3.6  grammes  a 
decimetre  length.  It  is  es- 
sential that  perfectly  dry 
wicks  be  used,  and  they  are 
commonly  kept  in  a  case 
containing  an  absorbent  of 
moisture. 


-47— * 

1 


i_ 


130.  The   flame   height   is 

not  specified  for  this  standard, 
for  its  unit  working  flame 
is  determined  only  by  the  Fia-  37- 

weight  of  combustible  consumed,  the  dimensions  of  the  chim- 
ney, and  the  height  of  the  wick  above  the  tube. 

131.  A  glass  chimney  of  the  ordinary  argand  shape  encloses 
the  flame.     The  thickness  of  the  glass  is  specified  at  two  milli- 

*  Audoin  and  B6vard;  ref.  cit. 


126  PHOTOMETEICAL  MEASUREMENTS 

metres,  but  this  is  a  condition  which  obviously  can  not  be  met 
with  precision  in  the  manufacture  of  glass  chimneys.  A  chim- 
ney, in  any  case,  introduces  uncertain  conditions — the  thick- 
ness and  absorption  of  the  glass,  and  the  reflection  of  light 
from  its  inner  surface,  are  not  capable  of  standard  and  unvary- 
ing definition. 

132.  Other  variations  are  due  to  the  charring  of  the  wick; 
this  being  rapidly  progressive  owing  to  its  free  height  above 
the  wick  tube.     When  the  lamp  is  lighted,  the  flame  increases 
to  a  maximum  illuminating  power,  and  then  decreases  with  the 
charring  of  the  wick. 

Another  condition  difficult  to  meet  is  the  maintenance  of  a 
prescribed  distance  between  the  top  of  the  wick  and  the  con- 
striction in  the  chimney. 

The  carcel  lamp  can  not  be  looked  upon  as  a  reproducible 
light  standard.  Kriiss,*  investigating  it  as  late  as  1894, 
stated  the  opinion  that  the  lamp  is  little  better  than  candles. 
Though  this  lamp  burns  with  a  greater  uniformity  of  flame 
than  a  candle,  and  the  light  strength  remains  fairly  constant 
during  a  measurement,  yet  the  wick  alone  causes  a  variation 
in  the  intensity  of  the  light  amounting  to  ±  10  per  cent  in  some 
extreme  cases. 

In  view  of  the  numerous  mechanical  sources  of  variation  in 
this  standard  of  light,  it  is  scarcely  necessary  to  consider  the 
added  influences  of  humidity  and  atmospheric  pressure. 

THE   METHVEN  SCREEN 

133.  Description.  —  The  Methven  standard,  in  its  later  form, 
consists  of  an  argand  gas  lamp  provided  with  a  light-reducing 
screen  (Fig.  38).     The  burner  is  a  plain,  argand  one  of  the 
Sugg  pattern,  and  is  surmounted   by  a  straight,  cylindrical 
glass  chimney,  two  inches  in  diameter  and  six  inches  in  height. 
To  the  base  of  the  lamp,  a  flat  or  concentric  plate  or  screen  is 

*  Schilling's  Journal,  1894,  page  614. 


STANDARDS   OF   ILLUMINATING   POWER 


127 


attached,  extending  upward  beyond  the  top  of  the  chimney, 

and  placed  1.5  inches  distant  from  the  axis  of  the  flame.     An 

opening  is  left  in  this  screen  opposite  the  centre  of  the  flame ; 

and  this  is  covered  with  a  thin  slide  containing  two  rectangular 

openings,  whose  longer  axes  are  placed  vertically.     Each  of 

these  apertures   is   of   standard   dimensions, 

adjusted  to  pass  a  light  flux  of  two  English 

candles'    intensity,    with   a  flame    height   of 

three   inches   for    the   smaller   one    and  2.5 

inches  for  the  larger.     The  slide  is  bevelled 

to  a  sharp  edge  at  the  openings ;  a  condition 

required  in  all  light  diaphragms.     In  order 

that  the  area  of  the  standard  aperture  shall 

not  change  by  corrosion,  it  is  cut  in  a  sheet  of 

silver.    All  the  metallic  parts  of  the  standard 

are  given  a  dull  black  finish. 

Two  apertures  are  usually  provided  in  the 
same  slide :  the  one  for  plain  gas,  and  the 
other  for  carburetted.  The  first  aperture  is 
0.233  inch  wide  and  one  inch  long;  and  the  second  one  is 
0.31  inch  wide  and  0.585  inch  long.  The  height  of  the  flame 
is  adjusted  by  means  of  sight  pins  projecting  on  either  side 
of  the  chimney  from  the  larger  screen. 

134.  Historical.  — It  was  announced  to  the  British  Association 
of  Gas  Managers,  in  1878,  by  John  Methven,*  that,  when  gas 
was  burned  in  similar  argand  burners,  at  a  given  flame  height, 
there  was  a  region  to  be  found  in  such  flames  which  would 
radiate  the  same  amount  of  light  for  unit  of  area,  or  have  equal 
intrinsic  brightness  of  flame  (page  31),  whatever  the  quality  of 
gas  might  be,  provided  the  combustion  was  complete.  He  had 
mapped  the  flame  length  by  means  of  a  transverse  slit  of  one- 
quarter  inch  width,  cut  in  a  concentric  metal  chimney  or  screen. 
The  position  of  this  slit  was  adjustable  vertically  that  it  might 
be  placed  opposite  any  desired  portion  of  the  flame.  Methven's 

*  Journal  for  Gas  Lighting  (London)  ;  32,  1878,  page  95. 


Fig.  38. 


128  PHOTOMETKICAL  MEASUREMENTS 

data  indicated  that  the  area  just  below  the  flame  centre  gave 
practically  uniform  light  emission  for  different  qualities  of  gas, 
provided  the  flame  height  was  three  inches,  the  combustion 
complete,  and  the  light  power  of  the  entire  flame  was  between 
fifteen  and  thirty-five  candles.  Possessed  of  this  knowledge  of 
gas  flames,  he  proceeded  to  adjust  the  dimensions  of  the  slit  so 
that  its  value  as  a  light  standard  should  be  two  English  can- 
dles. This  convention  has  been  uniformly  adopted  in  the 
manufacture  of  Methven  screens.  The  extreme  simplicity  of 
this  device  and  the  steadiness  of  the  light  source  so  com- 
mended this  standard,  that  its  use  became  general  both  in 
England  and  in  the  United  States.  In  this  country  especially 
it  has  been  widely  employed  by  incandescent  lamp  factories  as 
the  working  standard  for  the  photometry  of  their  product.  It 
has  proven  especially  useful  in  such  cases  because  of  the  con- 
stancy of  the  flame,  enabling  a  great  number  of  lamp  compari- 
sons to  be  made  in  a  short  time. 

It  was  soon  found  that  Methven  had  been  mistaken  in  his 
conclusions  regarding  the  unvarying  nature  of  the  standard, 
and  that  flames  of  the  same  dimensions  from  different  qualities 
of  gas,  and  varying  widely  in  the  quantity  of  light  emitted, 
contained  no  areas  of  invariably  constant  intrinsic  brightness. 

135.  The  Report  of  the  London  Board  of  Trade  in  1881.  —  A 
committee  of  this  organization,  after  testing  the  screen,  re- 
ported* that  they  found  the  Methven  screen  sensibly  constant 
only  for  the  limited  flame  variation  of  two  candles  for  any 
given  quality  of  gas.  This  result  was  to  have  been  anticipated. 
They  also  found  that  the  quality  of  the  gas  burned  was  of  the 
greatest  significance  and  induced  large  variations  in  the  value 
of  the  light  standard.  The  committee  concluded  that  the 
Methven-screen  standard  was  not  sufficiently  constant  and 
reproducible  to  serve  ,as  a  standard  of  light. 

A  number  of  equally  disparaging  reports  were  made  by  com- 
petent authorities  about  the  same  time,  and  Methven,  tooj 

*  Journal  of  Gas  Lighting  (London),  Oct.  25,  1881,  page  720. 


STANDARDS   OF   ILLUMINATING  POWER  129 

seems  to  have  concluded,  from  subsequent  tests,  that  he  had 
been  mistaken  in  the  supposed  principle  he  had  announced, 
and  had  in  reality  added  nothing  to  photometry  but  a  certain 
style  of  screen,  and  that  this  screen,  in  combination  with  an 
argand  gas  flame,  did  not  constitute  a  light  standard.  Appar- 
ently, in  order  to  support  the  apparatus  he  had  devised,  he 
looked  about  for  a  new  principle  with  which  to  endow  it. 

136.  Carburetting  the  gas.  —  Eventually,  Methven  was  led  to 
experiments  in  enriching  the  gas  supplied  to  the  burner  by 
means  of  a  volatile  hydrocarbon.  In  particular,  gasoline  seems 
to  have  yielded  the  best  results. 

The  illuminating  power  of  coal  gas  is  largely  due  to  the 
hydrocarbons  it  contains ;  and  if  a  gas,  low  in  its  hydrocarbon 
content,  is  led  through  a  suitable  reservoir  containing  gasoline, 
for  example,  it  becomes  enriched  to  a  corresponding  extent. 
On  the  other  hand,  a  gas  of  high  illuminating  power,  under 
similar  conditions,  absorbs  but  little  hydrocarbon  in  passing 
through  the  carburetor.  All  qualities  of  gas  when  passed 
slowly  through  a  carburetor  containing  gasoline  are  enriched 
to  such  an  extent  that  they  attain  approximately  equal  illumi- 
nating power.  These  facts  were  known  to  Methven  at  the  time, 
and  it  remained  for  him  to  test  their  accuracy.  He  was  thus 
led  to  make  a  second  announcement,  with  even  more  assurance 
than  accompanied  the  first,  that  his  researches  "prove  incon- 
testably  that  in  bringing  gases  of  extreme  range  of  quality  in 
contact  with  the  vapour  of  light  petroleum,  the  illuminating 
power  of  such  gases  is  equalized,  and  that  all  gases  consumed 
in  the  same  burner,  when  carburetted,  yield  the  same  illumi- 
nating power  of  flame."  * 

Undoubtedly  the  Methven  screen  used  with  carburetted  gas 
is  superior  in  results  to  its  employment  with  plain  gas;  yet 
this  combination  by  no  means  meets  the  requirements  for  a 
photometrical  light  standard,  in  that  the  combustible  is  too 
complex  and  uncertain  in  composition.  The  use  of  a  glass 
*  Journal  of  Gas  Lighting  (London) ;  40,  1882,  page  42. 


130  PHOTOMETRICAL   MEASUREMENTS 

envelope  for  the  flame  is  almost  fatal  to  the  employment  of 
such  apparatus  for  a  light  standard. 

In  1885,  W.  J.  Dibdin*  on  behalf  of  the  London  Metropoli- 
tan Board  of  Works,  made  elaborate  tests  upon  the  Methven 
screen,  using  plain  and  carburetted  gas.  His  conclusions  were 
especially  unfavourable.  A  committee  of  the  British  Associ- 
ation in  1888  indorsed  the  conclusions  of  Dibdin. f  The  later 
report  of  the  Dutch  Commissioners  was  even  less  favourable.  $ 

Methven  subsequently  subjected  his  proposed  standard  to 
closer  scrutiny  and  studied  the  influence  upon  it  of  tempera- 
ture and  atmospheric  pressure  and  humidity,  and  the  con- 
ditions under  which  the  carburetting  could  be  carried  out  to 
best  advantage.  His  work  led  to  no  improvements,  but  rather 
to  abandonment  of  the  screen  and  argand  burner  in  favour  of 
an  open  flame  jet  photometer. § 

137.  The  errors  due  to  the  use  of  a  screen.  —  Eawson  ||  called 
attention  to  the  application  of  the  law  of  inverse  squares  in  the 
distribution  of  light  from  a  standard  through  a  small  opening 
in  a  screen  placed  near  the  flame.  He  found  the  illumination 
of  the  photometer  screen  became  disproportionately  great  as 
the  screen  was  moved  toward  the  Methven  slit.  He  concluded 
that  the  sides  of  the  argand  flame  were  the  source  of  the 
errors,  and  that  in  consequence  the  law  of  inverse  squares 
could  not  be  rigidly  applied  —  as  in  the  case  of  open  flames. 

When  the  photometer  screen  is  placed  some  distance  from 
the  slit,  as  at  MN  in  Figure  39,  the  light-emitting  area  mn 
of  the  flame  may  be  regarded  as  a  sensibly  flat  surface.  Mov- 
ing the  screen  along  the  bar  to  PQ,  the  illuminating  area  of 
the  flame  is  laterally  extended  to  pq.  It  is  evident  that  the 

*  Journal  of  Gas  Lighting,  45,  1885,  page  718  ;  and  50,  1887,  page  290. 
t  British  Association  Report,  1888,  page  39. 
J  Journal  of  Gas  Lighting,  64,  1894,  page  1161;  serial. 
§  London  Gas  World,  Nov.  30,  1889,  page  597 ;   also  consult  Rawson 
Electrician  (London),  Oct.  15,  1886,  page  479. 
||  Electrician  (London),  Oct.  15,  1886,  page  480. 


STANDARDS   OF   ILLUMINATING   POWER  131 

illuminating  power  of  the  edges  of  the  flame  at  pq  is  greater 
than  at  the  limits  mn  .of  the  former  setting.  At  PQ,  then, 
the  screen  receives  a  disproportionately  greater  illumination. 
This  error  could  be  allowed  for,  by  platting  a  curve  of  screen 
illumination  applicable  to  all  screen  distances  that  are  found 
desirable.  A  better  suggestion  is,  that  the  distance  between 
the  Methven  standard  and  the  photometer  screen  be  main- 
tained at  a  fixed  value,  and  that  the  compared  light  be  moved 
for  accomplishing  the  equalization. 

M  P 


x 


Q 

FIG.  39. 

The  radiant  centre  of  the  Methven  standard  is  located 
neither  at  the  central  axis  of  the  flame,  nor  in  the  plane  of  the 
slit,  but  changes  for  each  position  of  the  photometer  screen. 

If  the  distance  from  the  standard  to  the  screen  is  great,  and 
the  area  of  the  screen  is  small,  then  the  law  of  inverse  squares 
may  be  applied  for  small  changes  of  the  distance,  measurements 
being  made  in  such  cases  from  the  surface  of  the  photometer 
screen  to  the  edge  of  the  slit. 

138.  Very  small  apertures  in  a  screen  for  a  standard  light 
simplifies  the  case  just  considered.     If  the  light  source  is  a 
plane  surface  (see  page  162)  and  the  aperture  is  very  small,  the 
law  of  inverse  squares  applies  with  sufficient  accuracy,  and  the 
radiant  centre  may  be  taken  in  the  plane  of  the  aperture. 

139.  Reflection  caused  by  a  glass  chimney.  —  That  portion  of 
the  chimney  back  of  the. flame  will  act  as  a  concave  cylindrical 
reflector,  and  the  radiant  centre  of  the  reflected  light  will  lie 


132  PHOTOMETRICAL  MEASUREMENTS 

back  of  the  reflecting  surface.  The  light  falling  on  the  pho- 
tometrical  screen  will  consist  of  light  directly  radiated,  the 
uncertainty  of  whose  centre  of  radiation  has  already  been  dis- 
cussed; and  in  addition,  the  screen  will  be  illuminated  by 
reflected  light  from  the  inner  walls  of  the  chimney  with  a 
radiant  centre  lying  back  of  the  chimney.  This  added  com- 
plication emphasizes  the  adoption  of  a  fixed  distance  between 
the  standard  and  the  photometrical  screen.* 

THE   PENTANE   STANDARD 

140.  This  title  is  applicable  to  two  distinct  types  of  light 
standards   that  are  to  be  carefully   distinguished  from   one 
another.     The  distinction  becomes  apparent  in  the  historical 
development  of  the  apparatus  from  the  earlier  air-gas  standard 
to  the  simpler  and  more  compact  pentane  lamps. 

141.  The  air-gas  pentane  standard.  —  The  original  memoir  on 
the  standard  was  presented  by  Harcourt  to  the  British  Associ- 
ation in  1877.|      After  detailing  tests  made  on  spermaceti 
candles  and  calling  attention  to  their  unsatisfactory  perform- 
ance,  he   describes  the   development   and    operation   of    the 
standard  which  has  subsequently  borne  the  name  of  the  Har- 
court pentane  standard. 

The  first  consideration  was  a  combustible  which  could  be 
readily  procured,  and  be  uniform  in  quality  and  of  a  simple 
chemical  nature.  For  this  standard  combustible  he  employed 
a  light  distillate  from  American  petroleum,  which,  after 
repeated  distillation,  finally  boiled  off  at  50°  Cent.  He  found 
the  liquid  to  consist  almost  entirely  of  pentane,  though  it  con- 

*  See  paper  by  B.  F.  Thomas,  Proceedings  International  Electrical 
Congress,  1893,  page  198. 

t  "  On  a  New  Unit  of  Light  for  Photometry,"  by  A.  Vernon  Harcourt, 
in  abstract  in  Proceedings  British  Association,  1877,  page  51 ;  and  printed 
at  length  in  the  Chemical  News,  36,  1877,  page  103 ;  also  in  the  Journal 
for  Gas  Lighting  (London),  30,  1877,  page  337. 


STANDARDS   OF   ILLUMINATING   POWER  133 

tained  small  amounts  of  other  paraffines  closely  approaching  it 
in  chemical  composition.  This  liquid  had  a  specific  gravity 
between  .6298  and  .6300,  and  by  analysis  he  found  it  to  contain 
83.3  per  cent  of  carbon  and  16.7  per  cent  of  hydrogen.  Being 
exceedingly  volatile,  he  determined  to  use  the  combustible  in  the 
form  of  a  vapour.  By  calculation  and  test  the  proper  proportion 
of  air  for  the  complete  combustion  of  the  vapour  was  determined 
to  be  20  volumes  of  air  to  7  volumes  of  pentane  vapour  at  60° 
Fahr.,  and  760  millimetres  atmospheric  pressure.  In  order  to 
prepare  the  air-gas  the  requisite  volume  of  air,  corrected  for 
humidity  and  atmospheric  pressure,  was  admitted  to  a  gas- 
holder over  water,  and  the  liquid  pentane  was  then  added ;  this 
almost  immediately  vaporized  and  rapidly  diffused  into  the 
contained  air,  and  in  a  short  time  the  mixture  of  air  and  vapour 
was  completed  and  ready  for  use.  He  further  found  that 
gaseous  paraffines  are  sparingly  soluble  in  water,  a  property 
which  rendered  pentane  eminently  suitable  for  such  purposes. 
The  behaviour  of  pentane  vapour  under  these  conditions  has 
been  fully  verified  by  subsequent  investigators,  who  have  found 
the  water  of  the  gas-holder  becoming  saturated  in  a  short  time 
with  pentane  vapour ;  the  air-gas  then  passes  through  the  gas- 
holder unchanged  in  proportions. 

142.  The  burner —  The  air-gas  was  burned  in  an  apparatus 
of  very  simple  construction.  The  burner  consisted  essentially 
of  a  brass  tube  one  inch  in  diameter  and  four  inches  in  length. 
This  tube  was  capped  by  a  brass  disk  one-half  inch  thick,  and 
perforated  centrally  by  an  opening  one-quarter  of  an  inch  in 
diameter,  such  a  large  opening  being  adopted  to  lessen  the  me- 
chanical error  in  the  reproduction  of  the  burner.  The  air-gas 
was  not  forced  through  this  opening  under  especial  pressure, 
but  was  allowed  to  diffuse  into  the  air  assisted  and  regulated 
by  its  own  gravity,  or  controlled  by  a  sensitive  pressure  regu- 
lator. 

Under  the  conditions  of  preparation,  and  at  the  pressure  and 
temperature  already  noted,  this  pentane  air  mixture  behaves  as 


134  PHOTOMETKICAL  MEASUREMENTS 

a  perfect  gas ;  a  fact  which  is  necessarily  fundamental  for  such 
a  standard  as  the  one  described. 

The  open  flame  thus  obtained  was  very  steady,  and  the  light 
was  especially  white  in  colour.  At  a  temperature  of  60°  Fahr. 
and  at  normal  atmospheric  pressure,  the  flame  maintained  a 
practically  constant  height  of  2T5g-  inches,  burning  the  air-gas 
at  the  rate  of  0.5  cubic  foot  per  hour.  The  dimensions  of  the 
apparatus  were  adjusted  to  yield  a  light  strength  equal  to  that 
of  the  spermaceti  candle,  burning  120  grains  of  combustible 
the  hour. 

143.  Tests  of  the  air-gas  standard.  —  In  order  to  assign  a 
proper  value  to  the  various  reports  on  the  pentane  standard, 
favourable  and  unfavourable,  which  will  be  noted  in  the  discus- 
sion, it  is  necessary  to  note  that  the  science  of  photometrical 
light  standards  has  made  rapid  advancement  toward  precision 
of  requirements,  especially  within  the  last  decade.  There  has 
been  within  this  period  a  decided  gain  in  accuracy  of  investi- 
gation, and  the  sources  of  variation  in  the  operation  of  light 
standards  have  been  subjected  to  closer  scrutiny  and  measure- 
ment. Though  these  various  reports  doubtless  represented 
opinions  justifiable  at  the  time  of  their  publication,  they 
are  no  longer  to  be  accepted  as  conclusive.  Their  chief  value 
at  present  concerns  the  logical  development  of  the  pentane 
standard.  These  observations  apply  similarly  to  the  discus- 
sion of  each  of  the  more  important  standards  of  illuminating 
power. 

A  committee  appointed  by  the  London  Board  of  Trade*  to 
test  the  reliability  of  the  various  light  standards,  after  studying 
the  behaviour  of  candles,  the  keats  lamp,  the  Methven  screen, 
and  the  Harcourt  air-gas  flame,  came  to  the  conclusion  that  the 
three  first  named  were  too  faulty  to  serve  as  photometrical  stand- 
ards of  illuminating  power ;  they  further  declared  the  Harcourt 
pentane  standard  to  be  satisfactory  and  sufficiently  constant  in 
operation  and  reproduction.  In  a  series  of  nineteen  measure- 
journal  of  Gas  Lighting  (London),  38,  1881,  page  719. 


STANDARDS   OF   ILLUMINATING   POWER  135 

ments  made  by  two  operators  working  independently,  the 
greatest  difference  between  the  values  found  was  1.8  per  cent. 
They  recommended  the  employment  of  the  Harcourt  air-gas 
standard  to  the  exclusion  of  the  others  named. 

In  1883  Harcourt  described  certain  improvements  in  the 
standard.*  Instead  of  mixing  the  gas  in  the  proportion  of 
three  volumes  of  air  with  1.05  volumes  of  vapour  in  preparation 
for  the  test,  he  introduced  liquid  pentane  into  a  gas  chamber 
from  a  suitable  reservoir,  through  a  device  which  enabled  the 
operator  to  control  the  rate  at  which  the  pentane  was  supplied. 
The  proportion,  then,  in  which  the  pentane  vapour  and  the  air 
mixed  was  entirely  under  control.  Harcourt  had  found  that 
the  height  of  the  flame  furnished  a  precise  indication  of  the 
proportion  of  the  air-gas  mixture.  By  these  improvements, 
instead  of  mixing  the  gases  in  a  definite  volume  ratio,  the  op- 
erator adjusted  the  flow  of  pentane  vapour  until  a  flame  height 
of  2.5  inches  was  reached ;  the  particular  height  denoted  the 
correct  proportion  of  air  and  pentane  vapour;  or,  in  general, 
under  the  conditions  of  burning  the  gas,  the  flame  height  was 
a  function  of  the  proportion  in  which  the  two  gases  were 
mixed.  Still  later,  additional  improvements  of  a  somewhat 
similar  character  were  made.f 

The  improved  Harcourt  standard  received  an  emphatic  en- 
dorsement by  a  committee  on  light  standards  of  the  British 
Association. $  In  1888  they  presented  a  report  which  was 
based  on  a  considerable  number  of  tests,  but  their  investigations 
seem  to  have  been  somewhat  deficient  in  thoroughness.  In 
detail,  the  report  stated  that  "the  pentane  standard  of  Mr. 
Vernon  Harcourt  is  reliable  and  convenient,  and  fulfils  all  the 
conditions  required  in  the  adoption  of  a  standard  of  light. 
This  standard  attains  this  end  by  its  having  no  wick,  and  con- 
suming a  material  of  definite  chemical  composition.  The 
experiments  of  your  committee  absolutely  show  that  the  light 

*  Proceedings  British  Association,  1883,  page  426. 

t  Journal  of  Gas  Lighting  (London),  49,  1887,  page  900. 

J:  Proceedings  British  Association,  1888,  page  41. 


136  PHOTOMETRICAL  MEASUREMENTS 

was  not  altered  when  the  specific  gravity  of  the  pentane  was 
.632  or  .628  instead  of  the  specified  value  of  .630." 

Prior  to  the  report  of  the  committee  of  the  British  Associa- 
tion, W.  J.  Dibdin*  on  behalf  of  the  Metropolitan  Board  of 
Works  had  made  a  series  of  painstaking  measurements  on 
standard  candles,  the  carcel  and  keats  lamps,  and  the  Har- 
court  air-gas  standard.  In  the  latter  case  he  investigated  the 
purity  of  commercial  pentane,  and  the  influence  of  its  impuri- 
ties on  the  illuminating  power  of  the  standard.  These  com- 
parative tests  resulted  favourably  for  the  pentane  standard,  and 
its  exclusive  adoption  was  strongly  recommended. 

The  comparison  standard  which  Dibdin  employed  was  a  gas 
flame  supplied  from  a  large  storage  tank,  on  the  supposition 
that  the  stored  gas  would  yield  a  constant  illuminating  power 
for  a  given  flame  height,  day  after  day.f  He  found,  however, 
that  gas  stored  over  clear  water  deteriorated  greatly ;  in  one 
case  it  amounted  to  lowering  the  illuminating  power  from  six- 
teen to  ten  units.  It  was  further  noted  that  after  a  certain 
interval  the  deterioration  ceased  and  the  gas  then  remained 
fairly  constant,  though  changes  in  the  temperature  of  the  stored 
gas  would  cause  variations  in  the  illuminating  power  of  the 
flame. 

From  the  difficulties  inherent  in  the  maintenance  of  a  stand- 
ard comparison  light,  it  is  apparent  that  results  obtained  from 
day  to  day  would  not  be  accurately  comparable. 

An  extension  of  these  tests  was  subsequently  made  and  in- 
cluded a  study  of  the  pentane  lamp  as  distinguished  from  the 
pentane  air-gas  standard.  In  this  later  form  the  standard  is 
simple,  practical,  and  easily  manipulated.  $  The  scientific 
value  of  Dibdin's  investigations  may  be  judged  from  the  fact 
that  they  were  endorsed  in  the  report  of  the  British  Associa- 
tion. § 

*  Journal  of  Gas  Lighting,  45,  page  673  ;  serial. 

t  Dibdin,  ref .  cit. ,  page  577. 

t  Journal  of  Gas  Lighting,  50,  page  290.    Compare  summary  on  page  143t 

§  British  Association  Report,  ref.  cit. 


STANDARDS   OF  ILLUMINATING  POWER  137 

THE  PENTANE   LAMP 

144.  The  air-gas  standard,  even  in  its  improved  form,  was 
strictly  a  laboratory  apparatus,  and  not  suitable  for  general  use. 
A  successful  attempt  was  subsequently  made  to  develop  it  into  a 
practical  standard  by  Harcourt  and  W.  S.  Rawson.*     In  this 
form,  known  as  the  Woodhouse  and  Rawson  pentane  lamp,  it  is 
essentially  a  spirit  lamp. 

145.  The  wick  extends  within  two  or  three  inches  of  the  point 
of  ignition,  and  has  less  significance  in  this  lamp  than  in  any 
other  light  standard.     So  long  as  it  is  clean  and  introduces  no 
foreign  matter  into  the  combustible,  and  preserves  a  sufficiently 
rapid  capillary  flow  of  the  pentane,  it  has  no  influence  whatever 
on  the  light  value  of  the  flame,  being  too  far  beneath  it  to  char 
when  the  lamp  is  burning. 

146.  The  production  of  the  flame.  —  The  pentane  delivered  by 
the  wick  is  vaporized  by  the  heat  of  the  wick  tube,  and  the 
vapour  ignites  at  its  upper  end.     The  outer  casing,  which  is 
constricted  at  this  point  to   a  diameter   of  20   millimetres, 
serves  as  a  chimney  and  screen  as  well,  for  the  base  of  the 
flame.     The  lower  part  of  the  upper  metal  chimney  is  similarly 
constricted  to  a  diameter  of  20  millimetres,  the  two  chimneys 
being   separated   to   a   distance   adjusted   by  an   appropriate 
gauge.     The  end  of  the  flame  is  sharply  pointed,  and  is  visible 
through  the  regulating  slits  in  the  chimney.     This  arrangement 
of  chimneys  constitutes  a  modified  Methven  screen,  the  open- 
ing between  them  being  so  placed  that  the  light  is  emitted  from 
the  central  portion  of  the  flame. 

147.  The  influence  of  the  heating  effects  in  the  operation  of  this 
lamp  is  especially  significant.     The  wick  tube  is  air-jacketed 
throughout  its  length  by  a  closed  outer  concentric  tube  in  order 
that  the  wick  tube  may  eventually  attain  a  constant  tempera- 

*  Journal  of  Gas  Lighting  (London) ,  61,  page  371.     British  Association 
Report,  1887,  page  617. 


138  PHOTOMETRtCA'L  MEASUREMENTS 

ture.  This  is  sufficiently  high  to  vaporize  the  highly  volatile 
pentane  at  a  point  some  three  inches  below  the  ignition  point 
of  the  flame.  The  third  or  outer  cylinder  acts  as  a  draft 
chamber,  and  passing  the  air  over  the  jacketed  wick  tube,  sup- 
plies it  to  the  flame,  heated  to  some  extent.  The  result  of  this 
arrangement  is  that  the  temperature  of  the  flame  is  increased 
very  considerably  above  that  of  an  open  pentane  flame  burning 
freely. 

These  features; — the  heated  air  supplied  to  the  flame,  and 
the  intense  heating  of  the  end  of  the  wick  tube — are  prime 
sources  of  the  variations  in  light  strength  and  the  unreliability 
of  the  pentane  lamp. 

148.  Description  of  the  ten-candle  pentane  lamp.  —  It  has  been 
seen  that  Harcourt  first  used  a  mixture  of  air  and  pentane 
vapour  for  the  combustible,  and  later  devised  a  lamp  in  which 
liquid  pentane  was  burned  with  a  wick.  Finally  he  has  pro- 
posed a  reversion  to  the  air-gas  type. 

Formerly  pentane  lamps  gave  a  light  intensity  of  one  or  two 
candles ;  but  a  greater  intensity  is  very  desirable.  To  obtain  a 
steady  and  compact  flame  having  a  luminqus  intensity  of  ten 
candles,  Harcourt  *  found  it  necessary  to  adopt  the  principle  of 
the  argand  burner.  The  use  of  a  glass  chimney  caused  such 
variations  in  the  intensity  of  the  light  that  it  was  finally  dis- 
pensed with,  and  an  open  flame  impinging  into  a  metal 
chimney  was  adopted.  This  later  lamp  differs  from  the  liquid- 
burning  lamp  chiefly  in  the  substitution  of  the  argand  principle 
for  the  simple  jet  flame.  The  ten-candle  lamp  was  adopted  by 
the  Metropolitan  Gas  Referees  of  London  as  the  official  standard 
of  illuminating  power,  and  in  consequence  of  this  official  sanc- 
tion it  merits  description  at  length. 

The  ten-candle  lamp  (Fig.  40)  employs  air  saturated  with 
pentane  vapour;  and  the  air-gas  so  formed  descends  by  its 
gravity  to  a  steatite  ring  burner.  The  top  of  the  flame  is  hid- 
den from  view  by  a  long  brass  chimney  A,  above  the  steatite 
*  Gas  World  (London),  28,  1898,  page  951. 


STANDARDS    OF    ILLUMINATING   POWER 


139 


burner  B,  while  a  mica  window  in  the  brass  tube  enables  the 
height  of  the  flame  to  be  gauged  and  adjusted.  The  chimney 
is  surrounded  by  a 
larger  tube  D  in  which 
the  air  is  warmed  by 
the  chimney,  and  so 
tends  to  rise,  making 
a  current  which,  de- 
scending through  an- 
other tube  E,  supplies 
air  to  the  centre  of  the  flame.  No 
glass  chimney  is  required  and  no 
other  means  need  be  employed  to 
drive  the  air-gas  through  the  tubes. 
The  saturater  8  is  connected 
with  the  burner  by  means  of  brass 
tubing,  though  in  the  first  lamps  a 
rubber  tube  was  employed.  In 
the  lower  end  of  the  connecting 
tube  is  placed  a  small  cock.  This 
should  always  be  opened  for  a 
minute  or  two  before  lighting  the 
lamp,  so  that  any  condensation  of 
pentane  which  may  have  gathered 
in  the  tubing  may  be  drawn  off. 
The  small  micrometer  cock  next 
to  the  base  of  the  burner  should 
be  kept  closed  during  this  opera- 
tion. When  the  lamp  is  in  use, 
both  cocks  on  the  saturater  box 
should  be  wide  open  and  the  height 
of  the  flame  be  regulated  by  the 
micrometer  cock.  The  saturater 
is,  at  starting,  about  two-thirds 
filled  with  pentane,  and  it  should 
be  replenished  from  time  to  time  FIG.  40. 


140  PHOTOMETRIC AL  MEASUREMENTS 

so  that  the  pentane  is  always  visible  through  the  glass  window. 
The  stopcock  /  for  admitting  air  should  be  fully  open  when 
the  lamp  is  in  use. 

The  lower  end  of  the  chimney  should,  when  the  lamp  is  cold, 
be  set  47  millimetres  above  the  steatite  ring,  and  this  adjust- 
ment is  tested  by  a  gauge  K9  which  is  provided.  The  exterior 
tube  D  communicates  with  the  interior  of  the  burner  ring  by 
means  of  the  connecting  box  above  the  tube  E  and  the  bracket 
F  on  which  the  burner  is  supported.  A  conical  shade  G  is 
placed  about  the  flame  and  is  so  adjusted  that  the  whole  sur- 
face of  the  flame  beneath  the  chimney  A  may  be  seen  through 
the  opening. 

149.  The  colour  of  the  flame. — Pentane  vapour,  being  espe- 
cially rich  in  carbon,  burns  with  a  brilliant  white  flame,  and 
burning  in  the  pentane  lamp  at  a  heightened  temperature  of 
combustion,  it  emits  a  very  satisfactory  quality  of  light,  and  one 
which  conforms  very  closely  to  the  requirements  for  a  pho- 
tometrical  standard  light.    This  property  especially  commends 
the  pentane  lamp  for  a  standard  of  illuminating  power. 

150.  The  flame  height  of  the  Woodhouse  and  Rawson  lamp.  — 
•The  interval  between  the  chimneys  being  adjusted  by  a  stand- 
ard gauge,  the  height  of  the  flame  is  regulated  by  adjusting  the 
wick  until  the  tip  of  the  flame  appears  vertically  at  the  centre 
of  the  regulating  slit. 

The  central  portion  of  the  flame  is  the  source  of  light,  the 
upper  and  lower  portions  being  screened  by  the  metal  chim- 
neys; this  arrangement  having  been  adopted  on  the  supposition 
that,  should  the  height  of  the  flame  vary  within  certain  limits, 
the  quantity  of  light  emitted  from  the  central  zone  would 
remain  practically  constant.  In  this  sense  the  pentane  lamp 
is  a  development  from  the  supposed  discovery  of  Methven, 
upon  which  he  based  the  design  of  his  screen.  Methven 
assumed  that  the  central  zone  of  a  gas  flame  of  definite  height 
emitted  a  constant  light  strength  independently  of  the  quality 


STANDARDS   OF   ILLUMINATING   POWEK  141 

of  the  gas  burned.  In  contrast,  Harcourt  assumed  that  in  the 
use  of  a  combustible  of  constant  quality,  the  central  zone 
emitted  a  constant  light  strength  for  varying  heights  of  the 
flame.  According  to  Harcourt's  tests,  this  assumption  was 
experimentally  verified.  It  is  now  known  that  this  assumption 
is  not  correct,  and  that  Harcourt' s  experiments  were  either 
lacking  in  sensibility,  or  were  in  error  from  lack  of  constancy 
in  the  comparison  light,  for  Liebenthal,  investigating  this 
matter  with  especial  care,  has  found  that  the  light  strength 
varies  considerably  with  the  flame  height.  For  flame  heights 
adjusted  either  to  the  top  or  bottom  of  the  slit,  or  at  inter- 
mediate points  of  -J,  i,  and  -|  of  its  length,  the  light  strengths 
were  in  the  proportion  of  97.9,  99.5,  100,  99.5,  97.9.*  These 
data  indicate  that  the  proper  adjustment  of  the  flame  height  is 
at  the  centre  of  the  slit,  and  that  the  flame  should  be  con- 
stantly maintained  at  this  height.  In  comparison  with  the 
open  and  unscreened  flames  of  the  candle  and  the  amyl  acetate 
lamp,  with  their  large  alteration  of  illuminating  power  for  a 
change  of  one  millimetre  in  flame  height,  the  change  in  the 
light  strength  of  the  pentane  lamp  of  about  0.4  per  cent  for 
each  millimetre  alteration  of  height  is  very  small,  and  in  this 
respect  the  pentane  lamp  exhibits  the  advantage  of  screening 
a  flame  and  confining  the  radiation  of  light  to  the  central  zone 
of  the  flame. 

151.  The  radiant  centre  for  the  light  does  not  lie  in  the  axis 
of  the  flame.  Harcourt  f  ascertained  experimentally  that  the 
law  of  inverse  squares  could  not  be  applied  to  this  screened 
flame  by  taking  the  radiant  centre  on  the  axis,  or  in  front  of 
the  flame ;  but  for  distances  from  it  not  less  than  ten  inches,  no 
sensible  error  resulted  from  taking  the  luminous  centre  midway 
between  the  axis  and  the  outer  tube.  This  was  subsequently 
confirmed  by  Liebenthal,  t  who  found  that,  taking  the  illumina- 

*  Electrotech.  Zeitschrift,  1895,  page  657. 

t  Journal  for  Gas  Lighting  (London),  51,  page  371. 

J  Liebenthal,  ref.  cit. 


142  PHOTOMETRIC AL   MEASUREMENTS  ... 

tion  of  a  unit  area  of  the  photometrical  screen  when  at  unit 
distance  from  the  radiant  centre,  at  L  units,  the  illumination 
Jj  when  the  screen  was  placed  at  a  distance  r  from  the  flame 
axis,  was 

(64) 


in  which  p  is  the  radius  of  the  constricted  portion  of  the  chim- 
ney about  the  flame,  and  L,  r,  and  p  are  expressed  in  terms  of 
a  common  unit  of  length. 

152.  The  influence  of  moisture  and  atmospheric  pressure. — The 
same  investigator  pursued  a  lengthy  series  of  tests  to  measure 
the  influence  of  the  humidity  of  the  air  and  the  atmospheric 
pressure  on  the  illuminating  power  of  the  pentane  lamp. 
The  comparison  standard  in  these  tests  was  an  incandescent 
lamp,  a  fact  which  makes  these  results  comparable,  and  imparts 
to  them  an  authority  not  inherent  in  the  work  of  earlier  investi- 
gators. The  effect  of  humidity  is  expressed  by 

y  =  1.232-  0.0068 ax*  (65) 

The  light  strength  y  is  stated  in  terms  of  the  amyl  acetate 
standard,  and  x  denotes  the  litres  of  moisture  in  the  cubic 
metre  of  dry  air  free  from  carbon  dioxide.  The  variation  in 
light  strength  caused  by  humidity  is  so  large  that  it  becomes  a 
marked  objection  to  the  use  of  such  a  light  standard.  How- 
ever, the  correction  factor  is  so  definitely  stated,  that  it  suffices 
to  use  a  satisfactory  hygrometer  such  as  an  Assmann,  at  the 
time  of  making  the  test.  The  equation  is  graphically  expressed 
in  Figure  41. 

The  variations  in  light  strength  consequent  on  changes  of 
atmospheric  pressure  are,  definitely  stated, 

A  y  =  0.00049  (&  -  760),  (66) 

*  Compare  this  formula  with  that  for  amyl  acetate  flames,  page  155. 


ANDARDS   OF   ILLUMINATING   POWER 


143 


where  b  is  the  reading  of  the  barometer  in  millimetres.  The 
corrections,  both  for  humidity  and  atmospheric  pressure 
changes,  are  so  significant  that  no  value  can  be  attached  to 
photometrical  measurements  with  the  pentaiie  lamp,  which  have 
not  been  accompanied  by  observations  of  the  barometer  and 
hygrometer. 


if 

*i 

l.Off 
1.04 
1.02 
1.00 
0.98 
0.96 

0.94 
0.92 

iJ 

~z~<~£ 

*J1 

1,25 
,1.23 

"X, 
1&- 

^ 

f*d 

^ 

^ 

i.i9 

^ 

^ 

1.17 

•^. 

^ 

1.15 

1_1  o 

^ 

^. 

:--„ 

^»*x 

^"^«» 

^^ 

"^^ 

1.09 

LITER 
DRY  A 

i  MOIS 
IR  FRE 

PURE 
E  FRO 

N  1  Cl 

«  CD2 

BIC  M 

:TE> 

^>v 

2            4            6           8           10          12          14         16         18          2( 
FIG.  41. 

153.  The  pentane  lamp  possesses  undoubted  value  as  a  light 
standard  in  certain  respects  pointed  out  in  this  discussion.  It 
has  two  marked  disadvantages,  which  cause  it  to  yield  prece- 
dence to  the  amyl  acetate  standard,  —  (1)  Pentane  is  one  of  a 
series  of  paraffines  whose  properties  are  so  similar  that  it  is 
exceedingly  difficult  to  obtain  it  free  from  admixture  with  other 
members  of  the  series,  and  consequently  the  combustible  for  the 
pentane  lamp  is  not  obtainable  as  a  definite  and  invariable  chem- 
ical substance ;  (2)  In  the  operation  of  the  lamp  the  temperature 
of  the  vaporizing  and  screening  tubes  continually  increases  until 
a  thermal  equilibrium  is  reached.  While  this  is  going  on,  the 
flame  gradually  lengthens,  and  must  be  lowered  by  depressing 
the  wick.  No  measurements  should  be  made  with  the  lamp 


144  PHOTOMETRICAL   MEASUREMENTS 

until  the  flame  height  becomes  constant,  which  ordinarily 
requires  about  thirty  minutes.* 

The  temperature  effect  is  not  confined  alone  to  altering  the 
flame  height,  but  the  intrinsic  brightness  of  the  flame  is 
increased  as  well,  as  this  is  a  function  of  the  temperature  for 
any  given  combustible.  It  is  these  things  especially  which 
render  the  pentane  lamp  ultimately  unsuited  for  a  standard  of 
illuminating  power.  These  strictures  should  not  be  applied 
peculiarly  to  the  pentane  flame,  but  they  are  applicable  to  all 
gas  flames  which  are  burned  in  envelopes  under  conditions 
which  cause  the  heating  of  the  burner  and  the  envelope. 

154.   The  report  of  the  Netherlands  Commission.  —  One  of  the 

most  recent  and  reliable  examinations  of  light  standards  has 
been  made  by  the  Dutch  Commission  on  photometry. f  They 
reported  a  decided  preference  for  the  mechanical  arrangements 
of  the  pentane  lamp,  but  advised  certain  modifications  in  its 
design,  and  the  use  of  a  mixed  combustible.  After  many 
experiments  they  determined  upon  the  proportions  by  weight 
of  nine  parts  of  benzol  with  one  hundred  parts  of  ethyl  ether. 
The  specific  gravity  of  the  standard  solution  should  be  0.7335 
at  15°  Cent. ;  of  the  benzol,  0.8860 ;  and  the  ethyl  ether  0.7215. 
They  reported  having  found  that  slight  impurities  in  the 
constituents  did  not  affect  the  light  value  of  the  standard. 

This  solution  did  not  burn  differentially,  as  might  be  sup- 
posed, from  its  behaviour  in  fractional  distillation,  but  was 
consumed  uniformly,  and  the  specific  gravity  of  the  combined 
liquid  in  the  lamp  was  that  of  the  original  solution.  This 
modified  standard  of  the  Netherlands  Commission  can  not  be 
regarded  as  an  improvement  over  the  pentane  lamp.  There 
appears  no  satisfactory  reason  to  justify  the  report  other  than 
the  desire  to  introduce  a  novel  or  peculiar  standard. 

*  Liebenthal,  ref.  cit. 

t  Journal  of  Gas  Lighting  (London),  1894,  page  1161 ;  also  Schilling's 
Journal,  1894,  page  613. 


STANDARDS   OF   ILLUMINATING  POWER  145 

THE   AMYL  ACETATE   LAMP 

155.  This  type  of  lamp,   frequently  termed  the   Hefner- 
Alteneck,*  or  simply  the  Hefner  lamp,  is  by  far  the  most 
noteworthy  of  all  the  existing  light  standards.      As  will  be 
developed  in  the  course  of  this  discussion,  this  standard  has 
been  subjected  to  accurate  and  thorough  investigation,  and  its 
faults  as  well  as  its  merits  are  clearly  understood.     The  worst 
feature  of  the  amyl  acetate  lamp  is,  perhaps,  the  colour  of  the 
flame,  and  no  other  photometrical  light  departs  so  far  from  the 
physiological  requirements  of  the  ideal  standard.     Its  wide 
currency  is  due  wholly  to  its  constancy  and  ease  of  repro- 
duction.    The  German  Commission  f  states  that  the  Hefner 
lamp  deserves  to  be  given  the  preference  for  excellence  over 
the  pentane  lamp,  a  statement  whose  significance  is  apparent 
in  view  of  the  action  of  the  Electrical  Congress  of  1893.  $ 

156.  The  Reichsanstalt   amyl   acetate   lamp.  —  The    Hefner 
lamp  was  modified  in  its  details  to  conform  in  the  design  and 
the  dimensions  of  its  parts  to  the  results  obtained  from  extended 
investigations  at  the  Physikalische  Eeichsanstalt.     This  form, 
commonly  known  as  the  Reichsanstalt  lamp,  has  been  univer- 
sally adopted  as  the  standard  one  for  the  use  of  amyl  acetate. 

The  lamp  is  shown  in  section  in  Figure  42.  The  material 
used  in  its  construction  is  brass,  with  the  exception  of  the  wick 
tube,  (7,  which  is  of  German  silver  to  avoid  corrosion  by  the 
combustible ;  and  for  a  similar  reason  the  walls  and  parts  in 
the  interior  of  the  lamp  should  be  thoroughly  plated. 

The  wick  is  moved  by  a  worm  gear,  ef,  which  actuates  two 
spur  wheels,  w  and  w^  All  the  fittings  of  the  lamp  are  attached 
to  the  cap  B,  which  unscrews  from  the  cup  A,  for  filling.  The 
cap  marked  D,  is  removed  when  the  lamp  is  in  use,  and  at 
other  times  it  should  be  kept  screwed  over  the  wick  tube. 

*  For  the  first  announcement  of  this  light  unit  see  a  paper  by  E.  von 
Hefner-Alteneck,  Elektrotech.  Zeitschrift,  1884,  page  20. 
t  Elektrotech.  Zeitschrift,  Oct.  10,  1895,  page  655. 
\  Proceedings  International  Electrical  Congress,  1893,  page  18. 
L 


146 


PHOTOMETRICAL   MEASUREMENTS 


The  dimensions  stated  in  the  figure  are  in  millimetres,  and 
certain  of  them  must  be  followed  with  great  accuracy.     This 


FIG.  42. 


is  especially  the  case  with  the  diameter  and  the  thickness  of 
the  wall  of  the  wick  tube,  and  the  flame  height  of  40  millimetres. 


STANDARDS   OF   ILLUMINATING  POWER 


147 


A  plate,  h,  moves  in  adjustment,  concentrically  with  the 
wick  tube,  and  carries  a  pillar  topped  with  the  Krtiss  optical 
flame  gauge,  shown  in  end  elevation  at  K  in  the  figure,  and  in 
side  elevation  in  Figure  43.  The  essentials  of  the  flame  gauge 
are  a  magnifying  lens  and  a  screen  of  ground  glass  fastened  in 


FIG.  43. 

the  eye  piece.     The  glass  screen  has  a  diametrically  horizontal 
scratch  on  it,  cutting  the  optical  axis  of  the  gauge. 

The  test  gauge,  Figure  44,  is  provided  for  the  verification  of 
the  flame  height  distance  from  the  top  of  the  wick  tube  to  the 
axis  of  the  flame  gauge.  It  is  placed  over  the  wick  tube,  and 
when  the  top  of  this  tube  is  viewed  horizontally  through  the 


148  PHOTOMETRICAL  MEASUREMENTS 

slits  in  it,  there  should  be,  for  correct  adjustment  of  the  height, 
the  slightest  observable  clearance.  The  top  of  the  gauge  is 
ground  off  to  a  slight  bevel,  giving  a  truly  horizontal  edge, 
which,  viewed  through  the  flame  gauge,  must  sharply  coincide 
with  the  scratch  on  the  glass  screen.  This 
most  ingenious  arrangement  of  gauges  enables 
the  operator  to  test  readily  the  accuracy  of  this 
very  important  dimension. 

In  England  this  standard  light  met  with  a 
tardy  reception.  The  Committee  of  the  British 
Association  on  light  standards,  in  their  report 
in  1888,*  while  calling  attention  to  the  con- 
stancy of  this  standard,  both  in  reproduction 
and  operation,  regarded  it  as  distinctly  inferior 
in  both  these  respects  to  the  Harcourt  pentaiie 
standard.  They  especially  criticised  the  red 
tinge  of  the  Hefner  light.  Disregarding  the 
influence  of  national  bias  in  each  case,  the 
conclusion  of  the  German  Commission  is  en- 
titled to  the  greater  weight,  being  not  only 
more  recently  formed,  and  hence  with  im- 
proved lamps,  but  being  based  on  more  thorough 
and  accurate  investigation. 

The  committee  on  units  and  standards  of  the  American 
Institute  of  Electrical  Engineers  has  recently  recommended  the 
Hefner  lamp  as  a  standard,  provided  it  is  certificated  by  the 
Physikalisch-Technische  Reichsanstalt.f 

157.  The  amyl  acetate.  — The  combustible  being  the  essential 
feature  in  the  production  of  any  photometrical  standard  flame, 
it  is  readily  seen  that  the  Hefner  lamp  derives  its  excellence 
from  the  chemical  simplicity  and  definite  composition  of  the 
substance  which  it  burns.  Amyl  acetate  is  a  colourless  liquid 
having  the  chemical  constitution  CgHnCs^Oa,  and  burns 

*  British  Association  Reports,  1888,  page  40. 

t  Transactions  American  Institute  Electrical  Engineers,  1897,  page  90. 


STANDARDS   OF   ILLUMINATING   POWER  149 

with  a  clear  flame,  rather  feebly  luminous  and  somewhat  red- 
dish in  colour.  It  is  prepared  commercially  from  the  distil- 
lation of  amyl  alcohol  obtained  from  fusel  oil,  with  a  mixture 
of  acetic  and  sulphuric  acids;  or,  by  distilling  a  mixture  of 
ethyl  alcohol,  sulphuric  acid,  and  potassium  acetate.  It  is 
extensively  used  in  the  arts  as  a  solvent  for  certain  colloids  and 
resins,  this  liquid  being  yellow  in  colour  and  quite  impure,  and 
entirely  unsuited  for  use  in  the  Hefner  lamp. 

158.  The  purity  of  the  amyl  acetate.  —  For  photometrical 
purposes  the  amyl  acetate  should  be  purchased  from  reliable 
dealers.  The  German  Gas  and  Water  Association  has,  with 
characteristic  care  in  such  matters,  assumed  to  furnish  amyl 
acetate  of  suitable  purity.* 

When  secured  from  other  sources  the  chemically  pure  variety 
should  be  specified,  and  before  using  it  certain  tests  of  its 
purity  are  to  be  applied.  The  tests  for  amyl  acetate  prescribed 
by  the  Physikalisch-Technische  Reich sanstalt  are :  f 

First,  the  specific  gravity  at  15°  Cent,  should  be  from  0.872 
to  0.876. 

Second,  when  distilled  in  a  glass  retort  at  least  ninety  per 
cent  should  pass  over  between  the  temperature  limits  of  137° 
and  143°  Cent. 

Tliird,  the  reaction  should  be  practically  neutral,  and  blue 
litmus  paper  not  be  sensibly  reddened  by  it. 

Fourth,  it  should  mix,  bulk  for  bulk,  with  ether,  benzine,  or 
carbon  bisulphide,  without  becoming  milky. 

Fifth,  a  clear  solution  should  result  upon  shaking  in  a  test- 
tube,  1  c.c.  amyl  acetate  with  10  c.c.  ethyl  alcohol,  ninety  per 
cent  Tralles,  and  10  c.c.  of  water. 

Sixth,  a  drop  placed  on  white  filter  or  blotting  paper  should 
evaporate  without  leaving  a  greasy  spot. 

The  amyl  acetate  should  be  kept  in  a  glass-stoppered  bottle 

*  This  is  to  be  obtained  from  Dr.  Bunte,  Karlsruhe, 
t  Zeitschrift  fur  Instruinentenkunde,  13,  page  257  ;    also  Schilling's 
Journal,  1893,  page  341. 


150  PHOTOMETRIC AL  MEASUREMENTS 

and  preferably  be  stored  in  a  dark  place,  as  it  has  a  tendency 
to  decompose  in  strong  light. 

Thus  specified,  the  amyl  acetate  is  sufficiently  pure  to  meet 
the  requirement  of  uniformity  in  the  composition  of  the  com- 
bustible, and  to  this  extent  the  Hefner  lamp  is  a  light  standard 
which  can  be  satisfactorily  reproduced.  The  foreign  substances 
liable  to  be  found  in  amyl  acetate  are  water,  amylic  and  ethylic 
alcohols,  but  none  of  these  in  the  proportion  liable  to  occur  in 
the  chemically  pure  acetate  of  commerce  has  a  sensible  effect 
on  the  illuminating  power,  according  to  tests  by  Hefner- 
Alteneck.* 

159.  The  wick.  —  The  character  of  the  wick  appears  to  be 
practically  without  influence  on  the  illuminating  power  of  the 
lamp,  provided  it  does  not  fill  the  tube  tightly ;  for,  owing  to 
the  low  vaporization  temperature  of  the  amyl  acetate,  the  wick 
does  not  usually  project  into  the  flame.  As  a  rule,  the  wick 
supplied  by  the  maker  of  the  lamp  is  a  woven  one,  though  a 
number  of  strands  of  candle  wick,  slightly  twisted  together, 
gives  satisfactory  results.  Loosely  woven  round  wicks  for  spirit 
lamps  are  entirely  satisfactory.  Should  the  notched  wheels  of 
the  regulation  Hefner  lamp  be  employed  to  move  the  wick  in 
the  tube,  a  woven  wick  will  be  preferable,  as  it  will  not  catch 
in  their  teeth.  In  any  case  the  wick  should  be  washed  in 
distilled  water,  then  soaked  for  a  time  in  a  one  or  two  per  cent 
solution  of  concentrated  ammonia,  and  finally  thoroughly 
washed  in  distilled  water. 

In  the  prescribed  model  of  the  Hefner  lamp  the  feeding 
wheels  are  actuated  through  a  worm-gearing;  if  this  is  care- 
fully made  with  broad  wearing  surfaces  it  is  satisfactory,  but 
in  many  lamps  the  workmanship  is  poor,  and  in  consequence 
the  gear  train  is  a  frequent  source  of  annoyance.  The  amyl 
acetate,  too,  especially  if  it  is  slightly  acid,  in  time  may  so 
damage  the  wearing  surfaces  that  the  train  will  not  work. 
Both  the  design  of  the  gear  train,  as  well  as  its  position  within 

*  Journal  of  Gas  Lighting  (London),  59,  1892,  page  296. 


STANDARDS   OF    ILLUMINATING   POWER  151 

the  bowl  of  the  lamp,  are  open  to  criticism,  and  the  arrange- 
ment should  be  improved  by  the  makers. 

It  has  been  frequently  stated  that  the  wick  does  not  char, 
but  this  is  in  part  misleading.  The  top  of  the  wick  does  char 
when  the  lamp  has  been  burned  a  short  time,  but  the  rate  of 
charring  is  so  low  it  does  not  materially  affect  the  illuminating 
power  during  a  short  period  of  burning.  Each  time  the  lamp 
is  used  the  wick  should  be  evenly  trimmed,  removing  all  loose 
ends  and  charred  portions. 

160.  The  wick  tube  and  test  gauge.  —  The  Physikalisch-Tech- 
nische  Keichsanstalt's  specifications  require  that  the  thickness 
of  the  wick  tube  shall  not  be  more  than  0.02  millimetre  larger, 
or  0.01  millimeter  smaller  than  the  normal  thickness  (Fig.  42), 
and  that  the  free  length  shall  not  differ  more  than  0.5  milli- 
metre, nor  the  inner  radius  more  than  0.1  millimetre  from 
normal  dimensions.  The  length  and  diameter  of  the  wick  tube, 
and  the  thickness  of  its  walls,  are  essential  from  the  influence 
of  the  heating  of  the  tube  on  the  light  value  of  the  flame. 

A  test  gauge  should  be  furnished  with  each  lamp  in  order 
to  standardize  the  flame  height.  When  the  gauge  is  properly 
fitted  on  the  top  of  the  lamp,  and  the  end  of  the  wick  tube  is 
viewed  horizontally,  a  mere  clearance  space,  not  exceeding  0.1 
millimetre,  should  be  visible  between  its  edge  and  the  bottom 
of  the  slot  in  the  gauge.  This  test  requires  great  care  to  avoid 
an  error  of  parallax.  Then,  looking  at  the  optical  gauge,  the 
upper  edge  of  the  test  gauge  should  sharply  coincide  throughout 
its  entire  length  with  the  line  scratched  on  the  ground  glass 
plate.  Since  the  variation  of  one  millimetre  from  the  normal 
flame  height  of  40  millimetres  will  cause  the  illuminating 
power  to  vary  by  nearly  three  per  cent,  it  is  evident  that  the 
conditions  above  outlined  will  require  careful  investigation. 

Bearing  in  mind  that  the  Hefner  lamp  burns  with  an  open 
flame,  and  granting  that  the  standard  was  satisfactory  in  all 
other  respects,  the  disproportionately  great  influence  which  the 
flame  height  and  the  dimensions  of  the  wick  tube  exert,  would 


152  PHOTOMETRICAL   MEASUREMENTS 

make  it  a  questionable  standard,  except  in  thoroughly  prac- 
tised and  skilful  hands. 

161.  The  colour  of  the  flame.  — The  amyl  acetate  flame  burns 
with  a  markedly  red  tinge.     According  to  the  criterion  estab- 
lished in  Chapter  I,  both  the  green  and  blue  colour  groups  are 
too  feebly  represented  for  it  to  be  even  approximately  a  stand- 
ard of  normal  illumination.     This  is  a  very  serious  disadvan- 
tage and  gives  rise  to  uncertainty  and  error  when  comparing  it 
photometrically  with  a  whiter  light.     In  this  respect  the  amyl 
acetate  flame  is  markedly  more  deficient  than  even  the  sper- 
maceti candle  flame. 

162.  The  flame  height.  — This  is  prescribed  at  40  millimetres 
above  the  edge  of  the  wick  tube,  and  this  particular  value  has 
been  selected  with  reference  to  the  most  constant  behaviour  of 
the  flame.     If  the  light  intensity  of  the  flame  corresponding  to 
a  height  of  40  millimetres  is  taken  as  unity,  then  the  intensities 
corresponding  to  the  flame  height  in  general  between  20  and  60 
millimetres  have  been  found  by  Liebenthal  *  to  be : 

Flame  heights,   20       25      30      35      40      45       50      60    millimetres 
Intensities,         0.38   0.55   0.70   0.85   1.00   1.12   1.25   1.50  units 

These  results  established  that  the  light  intensity  for  flame 
heights  above  40  millimetres  varies  as  a  linear  function  of  the 
flame  height  amounting  to  2.5  per  cent  for  each  millimetre 
change  in  height;  for  heights  less  than  40  millimetres  there 
was  similarly  a  linear  function  found,  in  this  case  amounting  to 
three  per  cent  for  each  millimetre  change  in  height. 

If  the  symbol  J  be  taken  to  denote  the  intensity  at  a  flame 
height,  h,  and  L,  the  intensity  for  the  normal  flame  height  of  40 
millimetres,  the  following  equations  express  these  linear  func- 
tions ;  for  flame  heights  between  40  and  60  millimetres  the  rela- 
tion is:  J=  L  |-1+0  025(^-40)]  ....  (67) 
and  for  flame  heights  between  20  and  40  millimetres : 

J=L  [1-0.030  (40-*)] (68) 

*  Elektrotech.  Zeitschrift,  1888,  page  97. 


STANDARDS   OF   ILLUMINATING  POWER  153 

The  tip  of  the  amyl  acetate  flame  is  sharply  pointed,  and 
through  its  feeble  luminosity  and  red  colour,  it  becomes  very 
difficult  to  locate  with  exactness  the  point  at  which  the  lumi- 
nous flame  ceases.  Nor  would  this  point  be  located  at  the  same 
place  by  all  observers,  owing  to  the  differing  degrees  of  sensi- 
tiveness of  eyes  to  light.  Even  though  the  optical  flame  gauge 
does  magnify  the  image  of  the  flame-tip,  there  is  a  large  per- 
sonal equation  and  limit  of  uncertainty  in  adjusting  the  flame 
height. 

163.  Reproducibility.  —  In  this  respect  the  Hefner  lamp  far 
excels  all  standards  which  have  come  into  general  use.     Upon 
summarizing  the  preceding  discussion,  it  is  found:  that  the 
combustible  is  chemically  simple  and  definite;    the  wick  is 
without  influence  on  the  light  value  so  long  as  it  is  clean  and 
is  not  compressed  to  the  extent  that  it  fails  to  feed  sufficient 
combustible  to  keep  the  end  of  the  wick  constantly  wetted. 
Other   details   are  merely  those  of  mechanical   construction, 
which,  owing  to  the  exactness  required  in  many  of  the  dimen- 
sions, should  be  of  the  very  best  character. 

The  Reichsanstalt  will  not  certificate  a  lamp  whose  illumi- 
nating power  deviates  by  more  than  two  per  cent  from  its 
standard  lamp.  This  limit  of  error  of  two  per  cent  is  apt  to  be 
misleading,  since  no  Hefner  lamp  can  be  relied  upon  within 
this  limit  by  all  observers.  Owing  to  the  added  influence'  of 
sources  of  variation  yet  to  be  discussed,  the  probable  working 
limit  of  reliability  is  seldom  less  than  five  per  cent.  However 
unsatisfactory  such  conditions  may  be,  it  must  be  admitted  that 
the  Hefner  lamp  is  far  less  unreliable  than  any  other  light 
standard. 

164.  The  influence  of  temperature.  —  The   Hefner  lamp  in 
burning  is  subject  to  two  sources  of  temperature  effects.     Its 
own  heat  of  combustion  will  produce  expansion  of  the  wick 
tube  and  other  parts,  but  variations  from  such  sources  are  ren- 
dered negligible  by  the  thinness  of  the  walls  of  the  tube  lead- 
ing to  rapid  radiation.     The  second  temperature  variation,  that 


154 


PHOTOMETRICAL  MEASUREMENTS 


of  the  atmosphere  surrounding  the  flame,  seems  to  exert  no 
discernible  influence  on  the  illuminating  power  of  the  flame. 

165.  Influence  of  atmospheric  moisture.  —  The  extent  to  which 
the  percentage  of  moisture  in  the  air  enveloping  the  amyl  ace- 
tate flaine  affects  its  light  value  demands  most  careful  attention 
on  account  of  the  magnitude  of  the  errors  introduced.  A  series 
of  accurate  tests  has  been  made  by  Liebenthal  extending  over 
a  sufficient  length  of  time  to  enable  him  to  express  the  value  of 
the  influence  of  atmospheric  moisture.*  The  annexed  table 
states  the  average  value  for  each  month  in  the  year,  but  in  any 
one  month  the  fluctuations  may  be  as  great  as  the  widest  dif- 
ference among  the  average  monthly  values.  This  would  be 
liable  to  occur  not  only  in  certain  months  of  the  year,  but  would 
probably  change  from  year  to  year.  In  short,  for  reliable 
measurements,  it  is  necessary  to  determine  the  humidity  of  the 
air  surrounding  the  flame  and  introduce  a  corresponding  cor- 
rection for  the  value :  — 

OBSERVED  MONTHLY  AVERAGES   FOR  LIGHT  VALUE  OF  HEFNER 
LAMP.     (Fig.  45.) 


Mean  Moisture  for  the  Month 
in  Litres,  per  Cubic  Metre 

Corresponding  Mean 
Light  Value 

January,  1895 
February     " 
March          " 

6.11 
5.25 
6.77 

1.016 
1.019 

1.01 

April            " 
May             " 
June            « 

9.14 
10.29 
12.31 

0.999 
0.994 
0.979 

July             " 
August        " 
September  " 
October       " 

14.43 
13.35 
11.07 
10.44 

0.970 
0.972 
9.986 
0.991 

November  " 

8.87 

1.000 

December   " 

7.18 

1.009 

Elektrotech.  Zeitschrift,  Oct.  10,  1895,  page  655. 


STANDARDS    OF    ILLUMINATING   POWER 


155 


The  greatest  variation  shown  by  this  table  was  between  101.9 
per  cent  and  97.0  per  cent,  or  a  change  of  4.9  per  cent  in  the 
illuminating  power.  The  tests,  however,  were  extended  over 
practically  two  years,  with  a  maximum  difference  noted  between 
103.3  per  cent  and  94.8  per  cent,  or  a  change  of  8.5  per  cent. 
The  conclusion  at  which  Liebenthal  arrived  was  that  so  far  as 


£2 
|3 

1.03 
1.01 
1.00 
0.99 
0.98 
0.97 

< 

^ 

\ 

\ 

/ 

tz 

^ 

\ 

J, 

/ 

\ 

A 

^ 

N 

^^ 

/ 

> 

j 

h 

cc 

HI 
CO 

1 

K 

ivnNvr 

\ 

1 

i 

i 

ui 

z. 

> 

3 

< 

CO 

I 

NOVEM 

i 

§ 

FIG.  45. 

atmospheric  moisture  is  concerned,  the  light  strength  of  the 
Hefner  lamp  can  be  relied  upon  within  a  mean  limit  of  the 
normal  light  strength  of  ±  4  per  cent.  The  equation  connect- 
ing these  results  is  for  humidity  between  three  and  eighteen 
litres  per  cubic  metre, 

y  =  1.049  -0.0055  x (69) 

y  being  the  illuminating  power  of  the  Hefner  lamp  at  a  humid- 
ity of  x  litres  of  moisture  to  the  cubic  metre  of  air  free  from 
carbon  dioxide.  These  same  relations  are  exhibited  graphically 
in  Figure  46.  From  the  equation  it  is  seen  that  when  x  is 


156 


PHOTOMETRIC  AL  MEASUREMENTS 


8.8,  a  unit  light  value  is  indicated.    The  significance  of  this  par- 
ticular value  for  the  humidity  will  be  pointed  out  later  on. 


OD 

Z 
3 
• 
M 

Z 

u. 

I 

1.04 
1.03 

1    (V) 

^ 

"""--. 

\ 

"^ 

^s 

^ 

^N» 

0.98 
0.96 

0.94 
0.92 

^ 

^ 

^^ 

^^> 

^ 

^ 



^ 

-•^ 

LITERS  MOISTURE  \H  1  Cl 
DRY  AIR  FREE  FROM  CO-. 

BIC  M 

TER 

24             6            8            10          13           U          16          18          20 
FIG.  46. 

166.  The  influence  of  carbon  dioxide.  —  The  same  investigator 
found  that  between  carbon  dioxide  contents  of  0.62  and  0.93 
litres  to  the  cubic  metre  of  the  air,  the  light  strength  varied 
through  0.2  per  cent.  With  good  ventilation  of  the  photo- 
metrical  room,  the  variations  in  the  light  strength  of  the  Hefner 
lamp  due  to  the  carbon  dioxide  content  of  the  air  should  be 
negligible. 

For  expressing  the  quantitative  relations  between  the  content 
of  carbon  dioxide  and  the  illuminating  power  there  exists  the 
equation 


2/^1.012-0.0072^ 


(70) 


in  which  x±  states  the  litres  of  carbon  dioxide  to  the  cubic  metre 
of  dry  air.  The  equation  further  shows  that  the  unit  value  for 
the  Hefner  light  is  taken  for  a  content  of  carbon  dioxide  of 
nearly  1.7  litres  per  cubic  metre. 

As  photometrical  rooms  are  often  small  and  usually  poorly 
ventilated,  the  moisture  and  carbon  dioxide  arising  from  the 


STANDARDS    OF   ILLUMINATING   POWER  157 

flames  under  test,  and  the  breath  of  the  experimenters  as  well, 
are  probably  responsible  for  a  considerable  share  of  the  errors 
and  uncertainties  to  which  ordinary  photometrical  measure- 
ments are  liable. 

167.  The  influence  of  atmospheric  pressure.  — Within  the  limits 
of  ordinary  variations  of  atmospheric  pressure,  Liebenthal's 
investigations  *  established  the  expression, 

Ay  =  0.00011  (6-760) (71) 

Ay  being  the  change  in  illuminating  power  of  the  amyl  acetate 
flame  based  on  unit  value  of  y  for  the  normal  atmospheric 
pressure  of  760  millimetres.  So  far  as  the  influence  of  baro- 
metric pressure  alone  is  concerned,  the  reading  of  the  barometer 
b  expressed  in  millimetres,  in  the  above  equation,  will,  by  its 
solution,  enable  an  accurate  correction  to  be  made  for  tests  at 
all  ordinary  atmospheric  pressures  other  than  normal.  Accord- 
ingly a  fall  of  the  barometer  of  25  millimetres  or  about  one 
inch,  would  decrease  the  luminosity  of  the  flame  only  about 
0.28  per  cent. 

This  is  another  addition  to  the  complexities  of  photometry 
with  open  flames,  and  emphasizes  the  desirability  of  a  standard 
free  from  such  disturbing  influences. 

In  view  of  the  number  and  value  of  the  influences  modify- 
ing the  light  strength  of  the  accepted  standards,  it  is  little  to 
be  wondered  at  that  the  photometrical  results  of  careful  and 
reliable  observers  should  be  so  wide  of  agreement.  Criticism 
should  not  be  made  against  either  the  knowledge  or  ability  of 
such  observers,  nor  the  resources  of  scientific  measurement,  but 
rather  there  is  necessitated  on  the  part  of  the  general  scientific 
public  a  broader  knowledge  of  the  obscurities  and  difficulties  of 
the  subject,  and  also  how  well-nigh  hopeless  is  the  attempt  to 
equate  physical  phenomena  against  psychological  events. 

*  Liebenthal,  ref.  cit. 


158  PHOTOMETRICAL  MEASUREMENTS 

168.  The  value   of  the  Hefner  unit. — Naturally  upon  the 
advent  of  the  Hefner  lamp,  and  the  recognition  of  its  import- 
ance, it  was  felt  to  be  desirable  to  express  its  illuminating 
power  in  terms  of  candles  or  carcels.     This  amounted  to  an 
attempt  to  express  definite  ratios  between  several  uncertain- 
ties and  another   only  somewhat  less  uncertain.      In  conse- 
quence, there  have  been  published  practically  as  many  values 
for  the  ratios  as  there  were  observers  who  had  attempted  the 
investigation. 

The  candle  power  of  the  Hefner  lamp  is  a  value  which  does 
not  admit  of  determinate  expression.  In  accordance  with  a 
custom  in  such  cases  a  ratio  will  be  presently  stated,  but  grant- 
ing its  accuracy,  the  ratio  only  obtains  for  the  particular  ex- 
periments from  which  it  was  deduced. 

169.  On  the  substitution  of  the  term  "Hefner  unit "  or  its  equiv- 
alent for  candle  power.  —  If  the  candle  is  an  unsuitable  light 
standard,  not  only  for  scientifically  exact  but  even  approximate 
photometrical  measurements,  the  term  "candle  power"  has  no 
definite  meaning,  and  its  use  is  questionable  as  the  name  for 
the  unit  of  the   illuminating  power  (refer  to  page   34).      A 
change  would  doubtless  be  made  without  hesitation  were  a 
thoroughly  scientific  and  generally  accepted  standard  of  light 
available.      The  term   "candle  power"  would  perhaps   give 
place  to  the  name  of  the  approved  unit,  based  on  the  standard 
adopted.     But  the  term  "  candle  power  "  being  meaningless  as 
a  quantitative  expression,  and  the  Hefner  unit  being  fairly 
concise,  it  might  be  advisable  to  follow  the  example  of  foreign 
photometricians  and  evaluate  illuminating  power  in  Hefner 
units*  or  its  equivalent. 

170.  The  significance  of  the  Reichsanstalt  certificate. — Prac- 
tically every  phase  in  the  construction  and  operation  of  the 
amyl  acetate  lamp  has  been  made  the  subject  of  thorough 

*  Report  stating  agreed-upon  names,  symbols,  and  dimensions  for 
photometrical  units.  Schilling's  Journal,  1897,  page  548. 


STANDARDS   OF   ILLUMINATING   POWER  159 

investigation  on  the  part  of  the  German  Gas  Commission  and 
the  Physikalisch-Technische  Keichsanstalt.  In  this  manner 
the  best  dimensions  have  been  determined  for  the  various 
essential  parts  of  the  lamp,  and  the  best  conditions  established 
under  which  to  operate  it.  Guided  by  this  thorough  knowledge 
the  Reichsanstalt  has  constructed  a  normal  or  standard  lamp 
with  which  other  lamps  offered  for  test  are  compared.  Certifi- 
cates are  issued  by  the  Reichsanstalt  upon  comparing  lamps, 
provided  their  structural  dimensions  are  within  limits  already 
referred  to,  and  the  illuminating  power  does  not  differ  from 
that  of  the  standard  lamp  more  than  two  per  cent.* 

The  certificate  means  that  such  a  lamp  will  reproduce  the 
Hefner  lamp  unit  within  two  per  cent  under  normal  atmos- 
pheric pressure,  and  with  average  humidity,  taken  to  be  8.8 
litres  of  moisture  to  the  cubic  metre  of  dry  air  and  normal 
average  carbon  dioxide  content,  provided  that  satisfactorily  pure 
amyl  acetate  is  burned,  and  the  lamp  is  properly  operated. t 

171.  General  directions.  —  In  order  to  prepare  the  lamp  for 
use,  insert  the  wick  into  the  wick  tube  and  test  the  adjusting 
wheel  train,  which  must  move  the  wick  easily  and  smoothly 
without  catching  in  its  threads,  or  sticking.  Then  the  top  of 
the  wick  should  be  trimmed  off  straight  and  smooth  with  the 
top  of  the  tube,  using  sharp  scissors  and  avoiding  irregularity 
of  surface  or  stray  thread  ends. 

The  top  of  the  lamp  is  unscrewed  and  the  amyl  acetate  is 
poured  into  the  lamp  until  it  is  nearly  filled,  leaving  sufficient 
space  that  the  addition  of  the  wick  will  not  cause  the  lamp  to 
overflow.  The  top  of  the  lamp  is  then  screwed  into  place,  and 
after  the  wick  has  become  thoroughly  wet,  the  lamp  is  lighted, 
the  flame  adjusted  to  normal  height,  and  the  lamp  is  placed 
permanently  in  position  on  the  photometer  bench.  According 

*  For  further  details  consult  Zeitschrift  fur  Instrumentenkunde,  13, 
1893,  page  257  ;  also  Schilling's  Journal,  1893,  page  341. 
t  Ibid. 


160  PHOTOMETRIC AL  MEASUREMENTS 

to  earlier  directions,  the  lamp  should  burn  freely  for  at  least 
ten  minutes  before  making  measurements  of  its  illuminating 
power,  but  wider  experience  with  the  lamp  has  shown  that  it  is 
better  to  extend  this  time  to  twenty,  or  even  thirty,  minutes, 
when  the  flame  will  certainly  have  attained  constant  luminosity. 
The  lamp  once  placed  should  not  again  be  disturbed. 

On  the  top  plate  near  the  wick  tube  a  few  small  vent  holes 
will  be  found,  and  these  must  be  inspected  and  kept  open.  The 
temperature  of  the  photometer  room  is  preferably  regulated 
between  15°  and  20°  Centigrade. 

The  lamp  is  not  to  be  used  in  a  close  or  small  room,  to  avoid 
excess  of  moisture  and  carbon  dioxide,  unless  rapid  ventila- 
tion can  be  had  without  creating  drafts  in  the  room. 

Immediately  upon  completing  the  measurements  the  lamp 
should  be  emptied  and  cleaned,  for  through  the  decomposition 
of  the  amyl  acetate  the  metal  parts  are  liable  to  corrosion; 
the  wick  should  also  be  removed,  and  the  lamp  and  wick  tube 
well  rinsed  with  ordinary  alcohol.  It  is  preferable  that  the 
wick  be  thoroughly  washed  in  clean  alcohol  and  then  dried 
and  stored  for  further  use.  A  convenient  place  for  keeping 
the  wick  is  a  tightly  stoppered  test  tube. 

It  is  not  advisable  to  use  the  amyl  acetate  emptied  out  of 
the  lamp,  a  second  time.  A  little  experience  will  enable  the 
filling  of  the  lamp  to  be  proportioned  to  the  length  of  the  tests 
so  that  little  need  be  wasted.  So  long  as  the  end  of  the  wick 
rests  in  the  amyl  acetate,  the  supply  is  sufficient  for  the  flame. 


PROPOSED   STANDARDS  OF   ILLUMINATING  POWER  — OR; 
THE  ARC  STANDARD  OF  LIGHT 

172.  In  the  operation  of  the  continuous  current  arc  lamp  a 
crater  forms  on  the  positive  carbon  which  become^  the  seat  of 
high  incandescence  of  the  materials  of  the  pencil,  and  is  the 
source  of  the  greater  portion  of  the  light  radiated  from  the 
arc.  A  flame  of  feeble  luminosity  compared  with  the  lumi- 


STANDARDS    OF   ILLUMINATING   POWER  161 

nous  power  of  the  positive  crater  extends  to  the  tip  of  the 
negative  pencil,  which  has  a  much  lower  temperature  than  the 
carbon  at  the  positive  end  of  the  arc.  The  constitution  of  this 
arc  flame,  as  well  as  its  illuminating  power,  have  been  subjects 
of  controversy  and  wide  difference  of  opinion. 

The  flame  has  been  regarded,  by  some,  to  be  composed  of 
very  minute  and  highly  incandescent  particles  of  carbon,  pro- 
jected from  the  positive  to  the  negative  carbon.  According 
to  another  opinion,  the  carbon  of  the  positive  crater  passes 
through  its  true  boiling  point  and,  vaporizing,  forms  the  arc 
flame. 

The  temperature  at  which  this  occurs  under  normal  atmos- 
pheric pressure  has  been  approximately  determined  to  be 
3500°  Cent.*  The  consensus  of  experimental  evidence  has 
satisfactorily  established  the  occurrence  of  true  ebullition  in 
the  electric  arc.  The  boiling  point  of  carbon  at  approximately 
3500°  Cent,  is  thus  a  physical  constant  of  the  same  significance 
as  the  boiling  point  of  water  or  the  melting  point  of  an  iron ; 
but  it  partakes  of  the  complexities  of  the  melting  point  of  an 
iron  rather  than  the  simplicity  of  the  boiling  point  of  water. 
These  complexities  originate  from  the  several  allotropic  forms 
in  which  carbon  may  occur  and  from  the  influence  of  the  hard- 
ness of  the  carbon  pencil. 

It  is  assumed,  but  not  yet  completely  demonstrated,  that  all 
forms  of  carbon  when  raised  to  the  temperature  of  ebullition, 
exist  in  the  atomic  grouping  which  is  characteristic  of  graphitic 
carbon.  On  the  latter  assumption,  all  forms  of  carbon  will  boil 
at  the  same  definite  temperature,  which  will  vary  only  in  pro- 
portion to  the  atmospheric  pressure. 

It  was  discovered  by  Abney  in  1878 1  that  the  intrinsic 
brightness  (page  31)  of  the  positive  crater  of  a  given  carbon 

*Violle,  Proceedings  International  Electrical  Congress,  1893,  page 
262  ;  also  Abney  and  Testing,  Proceedings  Royal  Society,  Vol.  35,  1883, 
page  331. 

t  Abney,  Proceedings  Royal  Society,  1878,  pages  157  and  161 ;  also 
British  Association  Report,  1883,  page  422. 


162  PHOTOMETRICAL   MEASUREMENTS 

was  constant  and  independent  of  the  watts  absorbed  in  the  arc. 
He  also  found  constancy  in  the  whiteness,  or  colour  grouping 
of  the  radiations  from  the  positive  crater. 

In  1892  it  was  independently  proposed  by  James  Swinburne 
and  S.  P.  Thompson  *  to  adopt  the  light  radiated  from  a  unit 
area  of  the  positive  crater  of  the  electric  arc  from  pure  car- 
bons, as  a  unit  of  standard  light. 

Violle,t  investigating  the  same  subject,  found  that  the  intrinsic 
brightness  of  the  positive  carbon  is  rigorously  independent  of 
the  power  expended  in  producing  the  arc  between  such  wide 
limits  as  500  and  34,000  watts.  He  also  examined  the  arc  with  a 
spectrophotometer  and  noted  that  the  brightness  of  any  partic- 
ular colour  group  or  wave  length  is  equally  independent  of  the 
power  absorbed  in  the  arc. 

Blondel  endeavoured  to  realize  a  working  arc  standard.:}:  He 
protected  an  arc  from  air  currents  in  a  suitable  box  and  placed 
before  it  a  water-cooled  screen  at  a  distance  of  2-3  centimetres 
from  the  crater.  This  screen  was  pierced  with  an  opening 
before  which  rotated  a  diaphragm.  In  such  a  case  it  suffices 
to  multiply  the  area  of  the  opening  in  the  diaphragm  with  the 
intrinsic  brightness  (page  31)  to  obtain  the  value  of  the 
standard  in  use.  The  value  found  by  this  investigator  for  the 
intrinsic  brightness  §  varied  between  150  and  163  candles,  || 
(Star)  though  Trotter  If  found  a  value  of  70  candles  (English) 
for  hard  carbons. 

In  use,  the  distance  from  the  light  standard  to  the  screen  is 
measured  (page  131)  from  the  diaphragm. 

Blondel  also  investigated  the  influence  of  the  carbons  on  the 

*  Proceedings  International  Electrical  Congress,  1893,  page  267  ;  also 
Philosophical  Magazine,  Vol.  36,  1893,  page  124. 

t  Reference  cited,  page  259. 

t  Proceedings  International  Electrical  Congress,  1893,  page  315. 

§  Reference  cited,  page  332. 

||  Violle  states  the  Star  candle  has  an  illuminating  power  equal  to  1. 15 
English  candles. 

IT  Proceedings  International  Electrical  Congress,  1893,  page  315. 


STANDARDS   OF   ILLUMINATING   POWER  163 

intrinsic  brightness  of  the  crater.*  As  was  to  be  supposed, 
he  noted  considerable  variations.  For  carbons  of  great  purity 
and  uniform  character  he  found  an  agreement  of  results  within 
two  per  cent.  The  values  obtained  with  soft  carbons  and  cored 
carbons  were  widely  different  from  those  obtained  when  hard 
carbons  were  burned.  He  found  cored  carbons  from  their  lack 
of  uniform  brightness  of  crater  were  unsuitable  for  such  stand- 
ard work.  On  the  other  hand,  a  cored  carbon  was  desirable  to 
maintain  the  crater  in  a  fixed  position. 

The  quality  of  the  carbon  —  its  hardness  or  softness,  amongst 
other  things  f  —  affects  both  the  quality  and  quantity  of 
light  emitted  by  the  arc  with  a  given  absorption  of  power; 
the  light  diminishing  in  quantity  and  becoming  bluer  with 
increasing  hardness  of  the  carbons.  The  entire  subject  of  the 
influence  of  the  character  of  the  carbon  on  the  quantity  and 
quality  of  light  radiated  from  the  arc  merits  more  complete 
investigation  than  it  has  hitherto  received. 

The  suggestions  to  employ  an  arc  standard  of  light  have  not 
yet  materialized  in  a  practical  form.  The  essential  question 
involved  is  similar  to  that  of  all  flame  light  standards,  —  the 
invariable  character  of  the  material  supplying  the  flame. 
With  the  possibility  of  producing  carbon  of  known  uniformity 
of  character  the  difficulties  involved  in  the  introduction  of  such 
a  standard  would  be  removed.  Standards  of  this  nature  would 
be  desirable  for  the  invariable  quality  of  the  light  emitted, 
provided  the  carbons  were  dependable,  and  for  the  added 
reason  that  it  so  nearly  corresponds  with  the  physiological 
requirements  of  the  eye.  The  arc  standard  of  light  is  an 
inviting  subject  for  further  investigation,  and  it  is  to  be  hoped 
that  renewed  efforts  will  be  made  to  obtain  reliably  uniform 
quality  of  carbons. 


*  Reference  cited,  page  329. 

t  W.  M.  Stine,  Electrical  World,  New  York,  Feb.  23,  1895,  page  223  ; 
April  6, 1895,  page  420  ;  also  Electrical  Engineer,  New  York,  Oct.  3,  1894, 
page  268,  and  Electrical  Review,  London,  Oct.  19,  1894,  page  460. 


164  PHOTOMETRICAL   MEASUREMENTS 

PROPOSED  STANDARDS  OF  ILLUMINATING  POWER 
INCANDESCENT  PLATINUM  STANDARDS 

173.  The  previously  discussed  standards  have  depended  for 
their  emission  of  light  principally  upon  the  incandescence  of  car- 
bon released  within  the  flanie  envelope  from  chemical  combina- 
tions.    The  incandescent  carbon  was  found  to  be  associated 
with  other  light-emitting  substances  such  as  luminous  gases, 
while  the  temperature  at  which  the  incandescence  of  the  flame 
constituents  occurred  was  modified  by  influences  whose  specific 
value  could  not  be  determined.     The  attempt  to  simplify  the 
character   of   the   light   standard  by  avoiding  the  indefinite 
modifying  influences  and  employing  a  suitable  and  simple  sub- 
stance for  the  incandescent  source  of  light  led  to  the  develop- 
ment of  the  platinum,  or  so-called  absolute  standards. 

174.  The  term  "absolute  standard"  employed  in  this  con- 
nection must  not   be  taken  to  imply  the  relations  which  it 
expresses   when  used  to   designate  a  class   of   very  precise 
measurements.     In  its  latter  use  it  refers  to  such  cases  in 
which  the  quantitative  relations  of  a  phenomenon  may  be  ex- 
pressed in  terms  of  constants  and  the  dimensions  of  length, 
time,  and  mass.     Applied  to  the  platinum  standard  it  implies 
that  the  light  strength  may  be  specified  by  reference  to  a  set 
of  conditions  which  are   completely  known   and   capable   of 
exact  definition.    This  use  of  the  term  "  absolute  "  is  a  question- 
able one,  and  may  prove  misleading,  for  were  the  standard 
realized  it  would  be  impossible  to  express  the  value  of  the 
light  strength  in  terms  of  the  dimensions  involved,  the  light 
strength  being  ultimately  a  physiological  and  not  a  physical 
quantity. 

175.  The  Violle  standard.  —  The  immediate  development  of 
the  incandescent  platinum  standard  proceeded  from  the  inves- 


STANDARDS   OF   ILLUMINATING   POWER  165 

tigations  of  Violle.*  The  selection  of  the  metal  was  guided 
by  the  considerations  that  the  molten  metal  should  not  oxidize, 
and  could  be  obtained  in  a  sufficiently  pure  state.  Silver  and 
platinum  were  especially  investigated,  and  the  latter  was 
finally  selected. 

A  vigorous  effort  was  made  to  secure  official  sanction  for 
the  Violle  standard  from  the  International  Electrical  Congress 
at  Paris,  in  1881.  In  the  final  action  on  the  subject  the  Con- 
gress retained  the  carcel  lamp  as  the  working  standard  of 
illuminating  power,  pending  the  action  of  an  international 
jury  which  it  recommended  should  be  appointed  to  pass 
finally  on  proposed  electrical  units,  and  determine  their  precise 
definitions.!  Such  a  jury  was  appointed,  and  a  renewed 
investigation  of  the  proposed  incandescent  platinum  standard 
was  made  in  cooperation  with  them. 

Although  the  investigation  of  the  subject  was  yet  in  its 
initial  stage,  and  had  not  been  generally  attempted,  and  the 
photometrical  adaptability  of  incandescent  platinum  was  by 
no  means  established,  the  jury,  assembling  for  final  action  on 
April  28,  1884,  in  a  conference  on  Electrical  Units,  adopted 
the  hypothetical  platinum  standard,  legally  defining  it  thus, 
"  The  unit  of  each  simple  light  is  the  normal  quantity  of  light 
of  the  same  kind  emitted  in  the  normal  direction  by  a  square 
centimetre  of  the  surface  of  molten  platinum  at  the  tempera- 
ture of  solidification.  The  practical  unit  of  white  light  is  the 
quantity  of  light  emitted  normally  by  the  same  source."  | 

The  spectrophotometrical  relations  to  a  standard  were  thus 
defined,  and  the  unit  for  illuminating  power,  and  the  standard 
of  normal  white  light. 

*  Annales  de  Chimie  et  de  Physique,  (6)  III,  page  73.  Platinum  ren- 
dered incandescent  by  an  electrical  current  was  studied  photometrically 
by  Zollner ;  Poggendorff's  Annalen,  100,  1857,  page  381 ;  and  109,  1860, 
page  256. 

t  Congres  International  des  Electriciens,  1881,  pages  331-359. 

|  Electrical  Review  (London) ,  May  10, 1884,  page  401 ;  also  La  Lumiere 
Electrique,  12,  1884,  page  270. 


166  PHOTOMETRICAL  MEASUREMENTS 

The  Violle  standard,  in  its  earlier  form  especially,  was  an 
expensive  apparatus,  requiring  about  a  kilogramme  of  plati- 
num.* A  large  amount  of  auxiliary  apparatus,  too,  was 
required  in  its  operation,  and,  in  consequence,  the  investiga- 
tion of  the  standard  has  not  been  general. 

The  platinum  was  melted  in  a  specially  formed  lime  crucible, 
by  means  of  a  compound  blowpipe  burning  oxygen  and  illumi- 
nating gas.  After  the  fusion  of  the  metal,  the  crucible  was 
moved  under  a  water-jacketed  screen,  pierced  with  a  circular 
opening,  whose  area  was  one  square  centimetre.  The  light 
emitted  from  the  molten  metal  was  reflected  by  a  mirror  to 
the  photometrical  screen,  and  balanced  against  a  carcel  com- 
parison lamp.  Advantage  was  taken  of  the  fact  that  a  molten 
metal  lowers  in  temperature  until  the  stage  of  solidification 
begins,  when  the  temperature  remains  constant  until  the 
process  is  completed.  Platinum,  too,  in  common  with  iron 
recalesces  brightly  during  solidification.  Violle  showed,  by 
following  the  cooling  with  a  thermopile,f  that  the  temperature 
remained  practically  constant  for  a  considerable  time  during 
solidification. 

As  the  metal  reached  the  point  of  solidification,  or  the  flash- 
ing point,  the  light  strength  increased  markedly,  and  the 
photometrical  screen  required  rapid  adjustment  to  obtain  a 
balance  while  this  condition  lasted.  This  setting  alone  was 
significant,  and  upon  it  the  value  of  the  standard  was  based. 
Usually  but  one  measurement  could  be  made  in  the  duration  of 
the  flashing,  and  it  was  necessary  to  fuse  the  platinum  anew 
each  time  a  measurement  was  desired.  This  proposed  stand- 
ard proved  not  only  tedious  to  operate,  but  required  great 
experience  and  a  high  degree  of  skill  to  obtain  results  of  any 
value.  Violle  states  $  that  the  quality  of  light  from  the  molten 
platinum  is  richer  in  violet  rays  than  the  light  from  the  carcel 
lamp. 

*  Measures  Electriques,  Eric  Gerard,  page  630 
t  Violle,  ref.  cit. 
t  Ibid. 


STANDARDS   OF   ILLUMINATING   POWER  167 

176.  Modifications  of  the  Violle  standard  were  attempted  to 
simplify  the  apparatus  and  decrease  its  cost.     Siemens's  modifi- 
cation appears  to  have  found  some  favour.     He  employed  a 
narrow  strip  of  platinum  foil  and  heated  it  to  fusion  by  an 
electrical  current.*     The  significant  measurement  of  the  light 
in  this  case  was  made  just  at  the  moment  of  fusion.     As  this 
occurs  suddenly,  and  the  radiating  surface  is  destroyed  by  the 
rupture  of  the  foil,  the  measurement  of  the  light  strength 
had  to  be  made  very  quickly.     As  the  platinum  approached 
the  melting  point  the  photometrical  screen  was  kept  continually 
in  balance,  until  the  light  failed,  when  the  last  setting  was 
taken  for  calculating  the  standard  light  strength. 

The  fusion  of  the  platinum  does  not  occur  at  such  a  uniform 
temperature  as  does  the  solidification.  The  temperature  of 
fusion  has  been  found  to  vary  depending  upon  the  past 
history  of  the  metal.  The  mechanical  effects  of  rolling  out 
the  foil  and  bending  it,  and  repeated  heating  short  of  fusion 
and  cooling,  may  cause  the  fusion  temperature  to  vary  con- 
siderably, and  in  consequence,  the  strength  of  the  light  emitted. 

Though  the  Siemens  apparatus  is  less  expensive  and  more 
easily  operated  than  that  used  by  Violle,  the  sources  of  error 
are  so  numerous,  and  the  errors  may  attain  such  magnitude, 
that  it  has  been  abandoned. 

177.  The  Reichsanstalt  investigations  conducted  by  Luinmer 
and  Kurlbaum  have  been  the  most  thorough  and  reliable  to 
which   the  platinum   standard  has   been   subjected.!      They 
found  that  the  slightest  impurity  in  the  platinum  caused  sen- 
sible variations  in  the  light  strength.     In  the  course  of  these 
investigations  the  character  of  the  impurities  found  in  platinum 
was  determined,  and  satisfactory  methods  were  found  to  render 
it  sufficiently  pure.t 

*  Elektrotech.  Zeitschrift,  1884,  page  245. 
t  Ibid.,  1894,  page  474. 

J  Mylius  and  Forster,  Zeitschrift  fur  Instrumentenkunde,  1892,  page 
93. 


168  PHOTOMETRIC AL   MEASUREMENTS 

Eventually  it  was  considered  advisable  to  abandon  the 
definition  of  the  light  standard  by  the  points  of  fusion  or 
solidification  of  the  platinum.  They  succeeded  in  obtaining 
a  definition  by  reference  to  a  fixed  temperature  short  of  fusion. 
Their  apparatus  was  so  complicated  and  required  such  skill 
for  its  manipulation  that  the  process  was  considered  unsuited 
for  the  definition  of  the  standard  of  light. 

The  report  to  the  British  Association*  in  1888  on  light  stand- 
ards, already  alluded  to,  stated  that  "Professor  Violle's 
standard  of  molten  platinum  is  not  a  practical  standard  of 
light."  Later  investigations  have  so  abundantly  confirmed 
this  decision  that  the  proposed  platinum  standard  is  no  longer 
considered  a  feasible  one. 


1 78.   On  the  contradictory  character  of  photometrical  data. —  The 

literature  of  photometry  is  singularly  conspicuous  for  discrep- 
ancies and  contradictory  numerical  data.  Methven's  supposed 
discovery  of  the  constancy  of  the  light  strength  in  the  central 
zone  of  a  gas  flame,  independent  of  the  quality  of  the  gas 
within  certain  limits,  and  Harcourt's  observations  on  the 
constancy  of  the  pentane  flame  through  slightly  varying 
heights,  were  each  established  by  tests  apparently  as  carefully 
performed  as  those  which  have  shown  these  assumptions  to  be 
erroneous.  Especially  when  the  voluminous  data  of  the  values 
of  the  illuminating  power  of  candles,  lamps,  and  gas  flame 
standards  are  compared,  the  variations  are  so  great  that  they 
bring  into  question  the  entire  subject  of  the  standards  of  light. 
Aside  from  such  causes  of  variation,  already  noted  in  the  dis- 
cussion, a  very  potent  one  has  been  the  variable  character  of 
the  light  with  which  these  comparisons  have  been  made. 

Prior  to  the  present  exact  knowledge  of  the  amyl  acetate 
and  pentane  flames,  there  was  no  accurately  reproducible  light 
strength  of  a  flame  to  employ  for  a  comparison  standard.  The 
comparison  lights  employed  were  kerosene,  carcel,  and  keats 

*  British  Association  Reports,  1888,  pages  40  and  47. 


STANDARDS   OF   ILLUMINATING   POWER  169 

lamps,  and  jet  and  argand  gas  flames.  The  measurements 
made  at  any  one  time,  while  they  might  be  comparable  amongst 
themselves,  were  not  so  with  measurements  made  at  any  other 
time,  from  the  lack  of  a  constant  and  reproducible  standard. 

How  comparable  would  measures  of  extension  prove  if  the 
unit  of  length,  the  foot  or  metre,  required  renewal  daily,  and 
was  not  reproducible  with  accuracy  and  constancy  ? 

It  was  not  until  the  incandescent  lamp  came  into  use  as 
a  secondary  standard  that  measurements  made  at  different 
times  became  comparable.  Through  the  constancy  of  the  light 
strength  of  the  incandescent  lamp,  observations  of  the  influence 
of  humidity  on  the  light  strength  of  flames,  extended  through 
the  entire  year,  became  possible.  The  investigations  made 
since  the  advent  of  the  incandescent  lamp  in  the  capacity  of  a 
comparison  standard  are  of  more  quantitative  value  than  all  that 
preceded  them,  and  their  data  may  be  accepted  with  a  confi- 
dence which  earlier  tests  did  not  inspire. 


THE   WORKING   VALUES   OF   LIGHT   STANDARDS 

179.  This  subject  has  invariably  proven  confusing  to  pho- 
tometricians.  The  values  found  in  various  treatises  and  peri- 
odical contributions  have  been  so  .wide  of  agreement  that  there 
appeared  no  grounds  for  the  selection  of  any  particular  value 
for  a  given  light. 

The  values  presented  in  this  paragraph  have  been  chosen 
for  the  reasons  that  they  were  obtained  by  extensive  experi- 
ments carried  on  probably  by  the  most  accurate  and  scientific 
methods  and  apparatus  recorded  in  the  literature  of  photom- 
etry ;  and  they  are  the  result  of  the  joint  labours  of  the  Ger- 
man Gas  Commission  and  the  German  Physical  Institute. 
They  were  selected  more  especially  because  the  incandescent 
lamp  was  used  as  a  comparison  standard  after  its  behaviour  for 
such  purposes  had  been  carefully  studied  and  its  constancy 
assured.  These  values  are : 


170 


PHOTOMETRICAL  MEASUREMENTS 


The  Paraffine  Candle  (Vereinskerze)  *    l_iojTf       TJ't 

at  a  flame  height  of  50  millimetres  > 
The  English  Candle*  at  a  flame  height  ?  _  i  14  TT  f  TT't 

of  45  millimetres  > 

The  Pentane  Lamp  f  set  with  one-candle  )  =  L17  Hefner  Units> 

gauge  y 

The  Hefner  unit  noted  here  is  the  light  strength  of  the  amyl 
acetate  lamp  adjusted  to  the  normal  flame  height  of  40  milli- 
metres under  the  atmospheric  pressure  of  760  millimetres,  and 
a  humidity  of  8.8  litres  of  moisture  to  the  cubic  metre  of  dry 
air  free  from  carbon  dioxide.  Stating  the  light  strength  in 
terms  of  the  normal  Hefner  unit  by  Z/,  and  the  litres  of  moisture 
in  the  cubic  metre  of  dry  air  free  from  carbon  dioxide  by  x,  the 
corrected  equation  of  the  amyl  acetate  lamp  is, 

L  =  1.049  -  0.0055  x  J  (72) 

and  similarly  for  the  pentane  lamp  it  is, 

L  =  1.232  -  0.0068  x.  $  (73) 

Reference  values.  —  The  comparative  light  strength  of  the 
French  decimal  candle  ||  with  that  given  by  other  recognized 
standards,  has  recently  been  determined  by  Laporte :  IT 


Decimal 
candle 

• 

Carcel 
lamp 

Heftier 
lamp 

Paraffine 
candle 

Decimal  candle   

1 

0.104 

1.13 

0955 

Carcel  lamp    

9.6 

1 

109 

92 

Hefner  lamp        •     •     •     •     • 

0885 

0092 

1 

0  815 

1.05 

0.109 

1.23 

1 

*  Schilling's  Journal,  1893,  page  342  ;  also  Zeitschrift  fur  Instrumen- 
tenkunde,  1893,  page  259. 

t  Liebenthal,  Elektrotech.  Zeitschrift,  1895,  page  655. 

J  Liebenthal,  ref.  cit. 

||  The  International  Electrical  Congress  at  Paris  in  1889,  gave  the  name 
of  bougie  decimals  to  the  twentieth  part  of  the  Violle  platinum  standard. 

1  Bulletin  de  la  Socie"t<§  Internationale  des  Electriciens,  May,  1898,  XV, 
page  181 ;  F.  Laporte. 


CHAPTER  V 

COMPARISON    LIGHTS,    OR     SECONDARY     STANDARDS 
OF  ILLUMINATING  POWER 

THE  INCANDESCENT  LAMP 

180.  This  source  of  illumination  is   not   only  the  especial 
object  of  photometrical  practice  in  electric  lighting,  but  it  pos- 
sesses additional  interest  from  being  a  proposed  light  standard ; 
and  is,  as  well,  of  unusually  great  value  as  a  comparison  light. 

In  this  latter  aspect,  certain  of  its  physical  characteristics 
demand  extended  discussion. 

181.  The  surface  of  the  filament  of  the  incandescent  lamp  may 
range  in  appearance  from  rough  and  dull  black,  to  polished 
smoothness  and  a  bright  gray  colour.      Whether  the  filament 
thread  is  silk  or  cellulose,  after  carbonization,  its  surface  will 
be  somewhat  irregular  and  dull  black  in  colour ;  this  is  remedied 
in  the  subsequent  process  of  flashing.*     As  generally  applied, 
the  process  consists  in  placing  the  filament  in  a  jar  containing 
an  atmosphere  of  a  volatile  hydrocarbon,  such  as  gasoline,  at  a 
pressure  of  about  one-quarter  of  an  atmosphere ;  there  the  fila- 
ment is  connected  in  circuit  and  the  voltage  is  increased  slowly 
until  the  filament  is  brought  to  a  white  heat.     The  hydrocarbon 
vapour  in  contact  with  the  filament  is  decomposed  and  deposits 
a  layer  of  carbon  upon  it.     The  deposited  layer  of  carbon  may 
vary  greatly  in  its  character- 

*  For  a  discussion  of  the  filament  and  processes  of  its  preparation,  refer 
to  Chap.  V,  The  Incandescent  Lamp  ;  G.  S.  Ram. 

171 


172  PHOTOMETRICAL  MEASUREMENTS 

The  influencing  causes  are  the  density  of  the  hydrocarbon 
atmosphere,  and  the  temperature  as  well  as  the  rate  of  deposi- 
tion. The  coating  is  hard,  smooth,  and  bright  gray  in  colour, 
when  the  flashing  has  taken  place  in  a  hydrocarbon  atmosphere 
of  low  density,  and  at  a  high  temperature,  slowly  applied. 
There  are  many  reasons  for  considering  such  a  gray  coating  to 
be  graphitic  carbon.  The  dull  black,  superficial  layer,  on  the 
contrary,  resembles  lampblack  in  its  properties. 

182.  The  emissivity  of  a  filament  is  affected  to  a  marked 
extent  by  the  character  of  the  superficial  layer  of  carbon.  In 
this  connection  certain  observations  made  in  the  first  chapter 
are  to  be  insisted  upon :  light  and  heat  waves  being  similar  in 
character,  yet  differ  in  frequency,  and  when  the  energy  of  the 
electrical  current  heats  the  lamp  filament  to  incandescence  there 
emanates  from  it  both  heat  and  light  radiations.  Were  it  pos- 
sible to  obtain  a  filament,  the  nature  of  whose  superficial  layer 
was  such  that  it  emitted  only  light  radiations,  all  the  electrical 
energy  expended  in  the  filament  would  be  transformed  into 
light,  producing  an  ideally  efficient  source  of  illumination. 
Again,  the  carbon  filament  may  be  heated  to  a  temperature 
short  of  incandescence  and  the  electrical  energy  supplied  be 
expended  in  heat  radiation.  While  noting  that  these  are  the 
limiting  conditions,  if  the  temperature  of  the  carbon  filament  be 
increased  until  it  becomes  incandescent,  there  coexist  radiations 
both  of  light  and  heat  energy.  The  emissivity  of  the  filament 
is  affected  to  a  marked  extent  by  the  character  of  the  superficial 
layer:  carbon  filaments  having  a  dull  black  surface  show  a 
higher  rate  of  emission  of  both  light  and  heat  energy  than  the 
bright  gray  filaments. 

Weber*  has  found  an  average  relation  in  the  emissive 
power  of  these  varieties  of  filament  surfaces  of  100  to  75.5  in 
favour  of  the  dull  black  one.  He  calls  attention  to  the  values 
of  the  radiating  power  for  lampblack  and  graphite  obtained  in 

*  Physical  Review,  1894,  page  116. 


COMPARISON  LIGHTS 


173 


the  classical  experiments  of  Leslie,  of  100  to  75.  The  conclu- 
sion then  follows  that  gray  filaments  are  at  least  coated  with  a 
layer  of  graphitic  carbon. 

In  general,  then,  the  flashing  of  carbon  filaments  usually 
results  in  a  coating  of  gray,  graphitic  carbon  with  lowered 
emissivity  of  the  filament,  having  a  lessened  rate  of  radiation 
both  for  light  and  heat. 

The  proportion  of  light  to  heat  radiation,  at  a  given  tempera- 
ture of  incandescence,  is  practically  the  same  for  both  the  dull 
black  surface,  and  the  gray,  graphitic  one,  though  it  requires 
less  expenditure  of  energy  to  maintain  this  temperature  in  the 
latter  filament  than  in  the  former  one. 

For  instance,*  a  filament,  which  before  flashing  and  at  a 
temperature  A,  gave  an  illumination  of  21  candles  with  84 
watts  expenditure;  when  flashed  and  again  operated  at  the 
temperature  A  the  relation  was  15  candles  for  60  watts.  By 
increasing  the  temperature  to  a  value  B,  the  initial  light  strength 
of  21  candles  was  obtained  for  68  watts  of  energy.  Had  the 
filament,  before  flashing,  been  operated  at  the  higher  tempera- 
ture B,  it  would  have  yielded  28  candles  for  about  90  watts  of 
energy  expended,  or,  tabulating  this :  — 


Filaments 

Candles 

Watts 

Watts  per  candle 

Black  j 
Gray    | 
Black  j 
Gray  | 

at  temperature 
A 
at  temperature 
B 

i 
i 

21 
15 
28 
21 

84 

60 
90 

68 

4 
4 
3.22 
3.24 

The  rate  of  emission  for  light  radiations  from  incandescent 
lamp  filaments  is  at  four  watts  for  the  candle  power,  from  100 
to  170  candle  power  for  the  square  inch  of  radiating  surface. 
This  may  be  increased  by  raising  the  temperature  to  the  point 


*The  Incandescent  Lamp;  G.  S.Ram,  page  63. 


174  PHOTOMETRIC  AL   MEASUREMENTS 

of  rapid  disintegration  of  the  filament,  to  about  1900  candle 
power  for  the  square  inch  of  emitting  surface.* 

183.  A  change  in  emissivity  due  to  repeated  heating.  —  The 

candle  power  of  an  incandescent  filament,  after  a  certain  epoch 
in  its  life  has  been  passed,  undergoes  a  marked  and  progressive 
change.  There  seem  to  be  a  number  of  causes  bringing  about 
this  result,  some  of  which  will  be  noted  later ;  but  the  imme- 
diate cause  is  a  change  in  the  emissivity  for  heat  and  light 
energy.  The  influence  of  prolonged  heating  increases  the 
emissivity  of  the  surface  of  the  filament,  and  the  change  is 
greatly  accelerated  by  increasing  the  pressure  on  the  filament 
above  what  may  be  considered  its  normal  voltage,  resulting  in 
an  increased  temperature  of  incandescence.  G.  S.  Ram  f  cites 
an  experiment  in  which  a  filament  had  been  operated  at  a  con- 
stant voltage  until  the  bulb  was  blackened.  He  then  found 
the  emissivity  had  increased  23.6  per  cent. 

184.  The  temperature   of    the   filament   with   the    differing 
varieties  of  commercial  lamps  has  been  generally  estimated  to 
be  between  1200°  and  1500°  Cent.     Weber,  $  by  measurements 
of  the  total  radiation,  and  taking  into  account  the  radiating  area 
of  the  filament,  has  been  able  satisfactorily  to  determine  its 
temperature.     He  found  the  general  practice  of  incandescent 
lamp  illumination  to  cover  a  range  extending  from  1127°  to 
1327°  (1400°  to  1600°  absolute)  Cent,  for  small  lamps ;  and  for 
larger  lamps  these  values  were  increased  by  50°.     The  relation 
between  the  temperature  of  the  filament  and  the  candle  power 
emitted  is  shown  graphically  in  Figure  47,  which  was  platted 
from  Weber's  data.     It  is  noteworthy  that  curve  A  relates  to 
a  flashed  or  gray  filament,  and  curve  B  to  one  having  a  black 
surface,  the  emissivity  of  the  black  filament  being  considerably 
greater  than  that  of  the  gray  one. 

*  G.  S.  Ram,  ref.  cit.,  page  64.  t  Ibid.,  page  199. 

|  Physical  Review,  1894,  p.  116. 


COMPARISON   LIGHTS 


175 


<f> 

I 

p 

s 

30 

/ 

/ 

«A 

/ 

4 

/  «. 

22.5 

/ 

7 

20 

/ 

/ 

/ 

/ 

15 

/, 

/ 

X 

^ 

10 

r^ 

.x; 

x^ 

7.5 

^: 

^ 

2.5 

-G»- 

.-  -— 

r--' 

-^ 

zzz 

S£> 

c 

:GRE 

ES 

•     1 

130  1 

0     £ 

0     C 

0     7 

0     i 

0     9 

0    10 

00    1 

0      i 

o    a 

0      j 

0     i 

0      t 

0      ' 

0     J 

0 

w  it 

00    J 

0 

20 

FIG.  47. 

185.  The  temperature    change   of   resistance  of   the    carbon 
filament  is  a  negative  one,  and  does  not  necessarily  have  the 
same   value   for    different    filaments.      The   flashing  process 
increases  the  value  of  the  temperature  coefficient  of  resist- 
ance.    The  relation  between  the  cold  and  hot  resistance  of  a 
lamp  is  then  an  uncertain  quantity,  depending  on  such  condi- 
tions as  can  not  be  exactly  determined. 

186.  The  hysteresis  of  the  resistance  of  the  filament.  —  When 
the  pressure  applied  to  a  filament   is  continuously  increased 
until  bright  incandescence  is  obtained,  and  then  continually 
decreased  at  the  same  rate,  the  resistance  corresponding  to  a 
given  candle  power  will  not  be  the  same  in  each  case,  being 
higher  in  the  first  instance,  and  lower  in  the  second,  than  a 
certain  intermediate  value,  which  would  be  obtained  by  keep- 
ing the  lamp  at  the  given  candle  power.     Or,  in  general,  for 
rapid  changes   in  the   pressure   applied  to   the   filament,  its 
change  of  resistance  lags  behind  the   change  in  volts.     The 


176  PHOTOMETBICAL  MEASUREMENTS 

amount  of  this  lag  varies  considerably  with  the  filament  tested. 
Usually  after  a  change  in  pressure  the  filament  attains  a  con- 
stant value  for  the  resistance  within  10  or  20  minutes.  The 
phenomenon  of  hysteresis  is  probably  due  to  some  molecular 
readjustment  within  the  filament. 

187.  The  vaporization  of  carbon  in  the  chamber  of  the  incan- 
descent lamp  is  now  generally  accepted  as  experimentally 
proven.  It  has  already  been  noted  (page  161)  that  in  the  case 
of  the  arc  light  the  carbon  reaches  its  boiling  point  and 
becomes  vaporized.  Although  one  of  the  most  permanent  sub- 
stances at  ordinary  temperatures,  carbon,  similarly  with  plati- 
num for  example,  when  rendered  highly  incandescent,  softens 
and  slowly  evaporates.  Evidences  of  such  action  are  seen  in 
the  blackening  of  incandescent  lamp  globes  and  in  the  shadows 
in  the  carbon  film  caused  by  the  legs  of  the  filament.*  There 
are  reasons  for  holding  that  evaporation  from  the  superficial 
layer  of  the  filament  must  go  on  to  some  extent  at  all  temper- 
atures of  incandescence,  though  it  is  not  until  the  filament  is 
heated  to  such  a  temperature  that  it  softens  that  the  rate  of 
evaporation  becomes  considerable.  At  any  temperature  the 
rate  of  evaporation  will  depend  on  the  character  of  the  super- 
ficial layer  of  the  filament,  hard,  gray  filaments  losing  less 
than  dull  black  ones.  The  immediate  effect  of  the  lessening 
of  the  cross  section  through  evaporation  is  the  increase  of  its 
resistance.  Weber  t  states  when  lamps  were  operated  for 
30  hours  below  a  certain  critical  temperature  the  resistance 
remained  practically  constant.  When  the  critical  temperature 
was  exceeded,  which  in  one  case  occurred  at  1330°  Cent.,  the 
resistance  rapidly  increased. 

Again,  the  critical  temperature  was  found  to  vary  with 
different  lamps,  showing  that  the  temperature  of  marked 
volatilization  varies  with  the  character  of  the  carbon. 

*  W.  A.    Anthony ;    Transactions  American    Institute  of    Electrical 
Engineers,  1894,  page  146  ;  also  W.  M.  Stine,  ref.  cit.,  page  181. 
f  Weber,  ref.  cit.,  page  210. 


COMPAEISON   LIGHTS 


177 


188.  A  study  of  unflashed  and  flashed  filaments. — Evans* 
has  made  a  remarkable  series  of  experiments  which  clearly 
develop  a  number  of  important  features  in  the  physics  of  the 
incandescent  lamp.  His  best  results  were  obtained  from  fila- 
ments apparently  made  from  parchmentized  paper,  purchased 
on  the  market  and  not  especially  made.  Though  they  are  of 
a  type  no  longer  in  use,  their  behaviour  is  in  keeping  with 
filaments  made  from  silk  and  cellulose.  As  purchased,  the 
filaments  were  black  in  colour,  with  a  rough,  untreated  surface. 

They  were  first  properly  mounted  and  the  bulbs  carefully 
exhausted,  and  then  subjected  to  photometrical  and  electrical 
measurements.  Subsequently,  they  were  removed  from  their 
chambers,  flashed,  remounted,  and  again  tested.  Finally,  they 
were  a  second  time  dismounted,  and  were  coated  with  a  rough, 
dull  black  layer  of  firmly  adherent  carbon  and  similarly  tested. 

The  data  of  the  several  tests  on  one  particular  filament  are : 


FILAMENT  FLASHED 

UNTREATED  FILAMENT 

IN  HTDKOCAKBON 

FILAMENT  FLASHED 

VAPOUR 

IN  COAL  GAS 

Candle 

Volts 

Current 

Watts 

Volts 

Current 

Watts 

Volts 

Current 

Watts 

power 

4 

45 

.86 

38.7 

34 

.95 

32.7 

39 

1.16 

45.2 

10 

56 

1.12 

62.7 

39 

1.12 

43.7 

44.5 

1.38 

61.4 

20 

62 

1.28 

79.7 

44 

1.28 

56.3 

49.5 

1.53 

75.7 

30 

66.5 

1.4 

93 

47 

1.47 

67.2 

40 

69 

1.48 

102 

49.5 

1.54 

76.2 

50 

71 

1.54 

109 

52 

1.67 

86.8 

60 

73.5 

1.62 

119 

52.8 

1.73 

91.3 

The  flashing  process  was  carried  on  slowly  in  an  atmosphere 
of  a  hydrocarbon  of  a  high  boiling  point.  In  this  treatment 
they  acquired  a  smooth,  highly  polished,  and  bright  gray  sur- 
face. The  subsequent  flashing  was  done  in  an  atmosphere  of 


*  Proceedings  of  the  Royal  Society,  40,  1886,  page  207. 

N 


178 


PHOTOMETRICAL   MEASUREMENTS 


coal  gas,  which  imparted  a  dull  black,  sooty-looking  coating, 
but  which  adhered  very  firmly  to  the  filament,  and  could  be 
handled  without  rubbing  off,  and  be  brought  to  high  incan- 
descence without  rapid  vaporization. 

Between  the  untreated  and  the  gray-flashed  surfaces  there 
was  apparent  at  any  given  candle  power  a  great  gain  in 
efficiency.  In  a  given  amount  of  energy  radiated,  the  propor- 
tion of  light  energy  to  heat  energy  emitted  was  considerably 
higher  with  the  gray  surface.  As  already  indicated,  Weber 
and  B,am  have  shown  that  in  such  cases  the  filament  with 
a  gray  surface  is  invariably  at  a  higher  temperature  of  incan- 
descence. The  gray  surface  has  a  lowered  emissivity  over 
the  black  one,  and  to  produce  an  illumination  equal  to  that  of 
the  black  surface  the  gray-coated  filament  must  be  operated  at 
a  higher  temperature.  The  gain  in  efficiency  is  not,  then,  due 
to  a  more  efficient  radiation  as  regards  light  rays,  at  a  given 
temperature,  but  that  in  consequence  of  reduced  emissivity, 
the  temperature  must  be  raised  to  produce  a  given  illumina- 
tion. The  gain  in  flashing,  however,  is  one  of  stability  of 
surface,  which  enables  the  filament  to  be  operated  at  a  higher 
temperature  without  producing  rapid  volatilization  of  the 
superficial  layers  of  carbon.  A  higher  temperature  of  incan- 
descence invariably  implies  an  increased  proportion  of  light 
energy  in  the  total  energy  radiated.  In  this  same  connection 
Evans  prepared  filaments  from  carbonized  fibre.  In  particular, 
one  was  mounted  with  a  black,  untreated  surface,  while  a  second 
one  was  flashed  to  a  bright  gray  surface.  These  filaments  were 
otherwise  alike  in  all  essential  respects  and  dimensions. 

When  tested  at  the  same  illuminating  power,  the  results  were ; 


Candle  power. 

Watts 

Watts  per 
candle  power 

Black  filament  . 

20 

100 

5 

Gray  filament    . 

20 

74 

3.7 

COMPARISON  LIGHTS 


179 


When  tested  under  conditions  of  nearly  equal  efficiency,  the 
results  were :  — 


Candle  power 

Watts 

Watts  per 
candle  power 

Black  filament  .  x'>        * 

28 

113 

4.04 

Gray  filament    .        •        • 

17.4 

71 

4.08 

Here,  again,  for  the  same  illuminating  power,  —  20  candles, 

—  the  gray  filament  shows  a  markedly  higher  efficiency  over 
the  black  one.     When  tested  at  the  same  temperature,  or  equal 
watts  for  unit  of  light  emitted,  the  superior  emissivity  of  the 
black  filament  was  clearly  shown,  for  the  gray  filament  exhibited 
but  62  per  cent  of  the  illumination  of  the  black  one. 

Such  results  apparently  indicate  that  at  a  given  temperature, 
black  and  gray  carbon  surfaces  have  the  same  proportionate 
emissivity  for  light  and  heat  rays,  though  the  total  emissivity 
of  the  black  carbon  is  greatly  in  excess  of  that  of  the  gray  one. 

189.  The  light  absorption  in  the  incandescent  lamp  is  a  factor 
which  can  not  be  assigned  a  known  influence.     The  thickness 
of  the  glass  walls  of  the  chamber  may  vary  not  only  amongst 
lamps,  but  in  any  one  lamp  from  paperlike  thinness  to  a  very 
considerable  thickness.     The  variations  in  the  character  of  the 
glass  and  in  the  thickness  of  the  walls  must  alter  the  amount 
of  light  absorbed  by  the  glass  envelope.      The  absorption  of 
light  is  still  further  increased  by  the  film  of  carbon  deposited 
on  the  inner  walls  of  the  envelope. 

190.  The  relation  between  illuminating  power  and  the  energy. 

—  The  incandescence  of  the  filament  is  a  function  of  the  energy 
transformed  within  it,  and  the  rate  of  energy  transformation 
is  the  most  important  defining  quantity  for  a  lamp. 

Primarily,  then,  the  fundamental  relation  for  an  incandescent 


180  PHOTOMETRICAL   MEASUREMENTS 

lamp  lies  between  its  light  radiation  or  illuminating  power  and 
the  energy^  producing  it.  Both  Abney*  and  Siemens  f  early 
investigated  the  dependence  of  the  radiations  from  the  filament 
on  their  influencing  factors.  Later  an  approximate  relation 
was  proposed  defining  the  illuminating  power  to  be  proportional 
to  the  cube  of  the  energy  transformed. 

In  what  follows,  P  will  denote  the  illuminating  power  in 
appropriate  units,  and  E  the  energy  in  watts,  while  m  and  n 
are  equating  constants.  The  approximate  formula  is: 

P=mE3.  (74) 

GotzJ  objected  to  this  formula  and  stated  that  a  curve 
platted  to  the  formula 

(75) 


conformed  very  closely  to  experimental  values. 
Working  from  the  exponential  formula 

P=mEx,  (76) 

Ferguson   and  Center  §   obtained  values  for  m  and  x  which 
varied  greatly  with  the  lamp  tested.     They  assumed  that  the 
coefficient  m  remained  unchanged  in  value  for  all  degrees  of 
incandescence.     That  this  is  not  the  case  will  be  shown  later. 
For  a  lamp  rated  at  110  volts  and  16  candles,  they  found 


P=98x  lO^X-E3.  (77) 

And  similarly  for  another  lamp  rated  at  100  volts  and  20  candles, 

P=110xlO-6x^2-7.  (78) 

Weber  ||  noted  that  his  measurements  conformed  fairly  well 
to  equation  74  stated  above.     He  did  not  find  the  coefficient 

*  Proceedings  of  the  Royal  Society,  37,  1884,  page  157. 
t  British  Association  Reports,  1883,  page  425. 
t  Centralblatt  fur  Elektrotechnik,  V,  page  720. 
§  Technology  Quarterly,  1891,  page  147. 
||  H.  S.  Weber;  rel  cit.,  page  198. 


COMPARISON   LIGHTS  181 

m  to  have  an  extendedly  constant  value,  but  in  general  it  in- 
creased with  the  intensity  of  the  illumination. 

191.  The  relation  between  the  illuminating  power,  the  current, 
and  the  electromotive  force.  —  In  applied  photometry,  as  well  as 
the  practice  of  lighting  with  incandescent  lamps,  regulation  is 
had  almost  entirely  with  reference  to  the  voltage ;  the  relation, 
then,  which  changes  in  the  illuminating  power  have  to  the 
voltage-change  is  important. 

Again,  as  in  the  case  of  the  energy  the  relation  of  illuminat- 
ing power  to  volts  is  given  with  sufficiently  close  approximation 

by  the  equation : 

P=aV*>  (79) 

V  denoting  the  volts  and  a  being  an  equating  constant. 

Ayrton  and  Medley  *  gave  as  the  result  of  certain  measure- 
ments 

P=«F«.  (80) 

Ferguson  and  Center  f  found  in  this  case 

P=62  xlO~14x  F6-6.  (81) 

They  also  determined  the  value  of  the  relation  between 
illuminating  power  and  current,  obtaining 

P=520/51.  (82) 

This  last  result  follows  from  the  same  method  of  analysis 
outlined  above. 

The  most  noticeable  fact  brought  out  by  these  results  is  the 
lack  of  comparableness  of  filaments  under  any  one  set  of  con- 
ditions. The  cause  of  this  must  be  in  the  filament  itself,  and 
the  physical  nature  of  such  carbon  is  evidently  complex  and 
not  within  exact  control. 

To  illustrate  these  various  relations,  data  are  here  given, 
obtained  from  an  incandescent  lamp  which,  at  104  volts,  was 

*  Philosophical  Magazine,  May,  1895,  page  421. 
t  Ferguson  and  Center  ;  ref.  cit. 


182 


PHOTOMETRICAL   MEASUREMENTS 


nominally  rated  to  yield  16  candles.     Curves   platted   from 


these  data  are  shown  in  Figure  48. 


Volts 

Milliamperes 

Watts 

Candle  power 

Watts  per  c.  p. 

65 

348 

22.6 

0.8 

28.3 

67 

370 

24.7 

1.3 

19.1 

69 

380 

26.2 

1.5 

17.5 

71 

390 

27;7 

1.8 

15.37 

73 

401 

29.2 

2.2 

13.35 

75 

412 

30.9 

2.6 

11.9 

77 

425 

32.7 

3.0 

10.9 

79 

438 

34.6 

3.6 

9.6 

81 

450 

36.4 

4.2 

8.68 

83 

461 

38.2 

4.85 

7.88 

85 

472 

40.1 

5.65 

7.1 

87 

486 

42.3 

7.00 

6.04 

89 

497 

44.2 

8.00 

5.54 

91 

508 

46.3 

9.2 

5.03 

93 

516 

48.0 

10.2 

4.70 

95 

529 

50.3 

11.05 

4.55 

97 

541 

52.5 

12.6 

4.16 

99 

552 

54.6 

14.5 

3.76 

101 

564 

56.9 

16.3 

3.44 

103 

575 

59.2 

18.0 

3.29 

104 

580 

60.3 

18.8 

3.20 

105 

586 

61.5 

20.2 

3.05 

107 

597 

63.9 

22.0 

2.90 

109 

608 

66.3 

25.5 

2.60 

111 

620 

68.8 

28.0 

2.45 

113 

631 

71.3 

30.5 

2.34 

115 

642 

73.8 

32.7 

2.25 

117 

653 

76.4 

35.5 

2.15 

119 

665 

79.2 

39.3 

2.00 

121 

680 

82.3 

43.0 

1.91 

123 

690 

84.9 

47.5 

1.79 

125 

703 

87.9 

50.0 

1.76 

127 

717 

91.1 

55.0 

1.65 

COMPARISON   LIGHTS 


183 


716      10      12.5     1,5      17.5     20      22.5 


FIG.  48. 

192.   The  life  characteristics  of  the  incandescent  lamp. — The 

curve  of  the  maintenance  of  illuminating  power  throughout  the 
life  of  the  filament  is  a  valuable  indication  of  the  extent  to  which 
the  physical  condition  of  the  filament  has  changed.  In  the 
same  connection  the  energy  curve  for  the  unit  of  illuminating 
power  affords  some  indication  of  the  maintenance  of  the 
rate  of  emission  of  radiations  from  the  filament.  In  this  case 
the  measure  of  the  light  radiated  is  taken  as  an  approximate 
measure  also  of  the  dark,  or  heat,  radiations.  But  the  light 
and  heat  radiations  are  not  functions  of  each  other,  so  the 
curve  of  watts  for  sustained  candle  power  does  show  a  change 


184 


PHOTOMETRICAL   MEASUREMENTS 


in  the  rate  of  emission  without  affording  a  quantitative  deter 
mination  of  it. 


50  100  150  200  350  300  350  400  450  500  550  600  HOURS 
FIG.  49. 

A  number  of  curves  are  shown  in  Figure  49  for  a  test  extend- 
ing through  600  hours.  New  lamps  were  employed,  and  main- 
tained in  continued  incandescence,  and  the  voltage  was  kept 
practically  constant  at  the  marked  values  for  the  lamps.  The 
lamp  A  was  rated  for  100  volts,  the  others  for  110  volts,  and 
each  had  a  nominal  illuminating  power  of  16  candles.  The 
lamp  A  to  a  marked  extent,  and  the  lamp  B  to  a  less  degree, 
exhibit  an  initial  increase  of  illuminating  power,  which  reached 
a  maximum  value  between  50  and  75  hours.  This  was  fol- 
lowed by  a  continuous  decrease,  but  the  decrement  was  not 
uniform  until  300  hours  had  elapsed.  It  is  very  noticeable  in 
all  the  curves  that  the  epoch  from  150  to  250  hours  is  charac- 
terized by  the  least  slope  of  curvature,  or  the  illuminating 
power  is  more  nearly  uniform  during  this  epoch  than  any 
other.  In  contrast  with  the  curves  from  lamps  A  and  B,  the 
curve  from  the  lamp  O  exhibits  a  continual  decrease  in  illumi- 


COMPARISON   LIGHTS  185 

nating  power.  In  the  lamp  D,  the  initial  illuminating  power 
°ell  off  rapidly  and  then  increased  as  quickly,  until  the  illu- 
minating power  was  partially  recovered;  thence  the  curve  in 
general  resembles  the  others. 

The  filaments  of  the  lamps  whose  life  curves  are  marked  A, 
13,  and  (7,  were  of  the  squirted  cellulose  varieties.  Lamps  A 
and  B  were  from  the  same  maker. 

The  following  details  have  been  furnished  by  the  manufac- 
turers of  these  lamps  :  * 

"  The  purest  obtainable  form  of  cellulose  [A  and  B,  cotton] 
is  dissolved  in  a  solution  of  zinc  salts  [A  and  B,  ZnCl2],  which 
at  the  proper  temperature  forms  a  stiff,  gluelike  liquid.  This 
liquid  is  forced  through  a  glass  die  into  a  glass  jar  containing 
an  alcoholic  coagulating  solution  \_A  and  B,  alcohol],  when  it 
hardens  into  a  thread,  resembling  vermicelli,  which  coils  upon 
a  plate  near  the  bottom.  When  a  sufficient  length  of  thread 
has  been  squirted,  it  is  removed  and  washed  thoroughly  in 
much  the  same  way  that  a  photographic  plate  is  cleansed  after 
development.  After  washing  out  the  soluble  zinc  salts  and  the 
alcohol,  nothing  remains  but  non-fibrous  or  amyloid  cellulose 
in  the  form  of  a  soft  thread.  In  this  stage  it  is  weak  and  tears 
readily.  The  thread  is  then  wound  upon  reels  and  allowed  to 
dry  at  a  constant  temperature.  In  drying  an  enormous  shrink- 
age occurs,  the  diameter  of  the  thread  being  reduced  to  about 
one-fourth  that  of  the  die  through  which  it  was  squirted.  The 
size  of  the  thread  suitable  for  each  kind  of  lamp  is  controlled 
by  the  size  of  the  die. 

"These  dried  threads  are  then  wound  upon  forms  of  a  size  and 
shape  to  give  the  requisite  number  of  coils  of  proper  diameter 
for  the  filaments  desired. 

"The  wound  forms  are  next  placed  in  graphite  boxes  and  sur- 
rounded with  powdered  carbon.  The  boxes  are  subjected  to  a 

*  The  writer  acknowledges  his  obligations  to  the  courtesy  of  the  manu- 
facturers of  these  lamps,  especially  to  the  company  making  lamp  C,  by 
whom  this  description  was  furnished. 


186  PHOTOMETRICAL    MEASUREMENTS 

temperature  sufficient  to  soften  platinum  in  a  furnace  which  is 
slowly  heated  until  the  highest  point  is  reached.  The  heating 
requires  about  eighteen  hours,  and  must  be  very  gradually 
applied  until  the  hydrocarbons  are  removed  from  the  thread, 
otherwise  they  will  melt  together. 

"  After  the  baking,  nothing  remains  but  pure  carbon,  weighing 
about  one-fourth  as  much  as  the  threads,  and  representing  the 
fixed  carbon  of  the  cellulose.  In  this  condition  the  carbons 
resemble  a  japanned  steel  spring.  They  are  very  hard  and 
elastic,  though  brittle,  and  are  quite  uniform  in  size  and  resist- 
ance. A  coating  of  carbon  is  deposited  upon  these  carbon 
wires  by  heating  them  electrically  in  the  vapour  of  a  liquid 
hydrocarbon  \_A  and  _B,  gasoline].  As  the  deposition  or  treat- 
ment of  each  carbon  is  under  control,  the  current  is  cut  off 
automatically  when  the  diameter  and  resistance  have  both 
reached  the  points  suitable  for  the  kind  of  lamp  for  which  it  is 
designed.  After  ' treating,'  the  colour  of  the  filament  is  a  steel- 
gray,  due  to  a  coating  of  what  is  probably  graphitic  carbon.'7 

The  filament  which  yielded  the  best  results  in  these  tests 
was  of  the  cellulose  type,  made  in  the  usual  manner  by 
dissolving  cotton  in  a  solution  of  ZnCl2,  and  then  squirting  this 
under  air  pressure  through  a  die,  into  alcohol.  After  the 
artificial  thread  was  carefully  washed  and  dried  on  a  drum,  it 
was  wound  on  a  form  and  carbonized  in  the  usual  manner,  and 
finally  flashed  in  gasoline  vapour. 

The  first  three  curves  indicate  careful  manufacture  and  satis- 
factory flashing,  while  the  last  curve  shows  an  unstable  con- 
dition of  its  filament,  characteristic  of  faulty  manufacture. 

The  subject  of  life  tests  on  incandescent  lamps  has  been 
frequently  and  widely  experimented  upon  with  fairly  uniform 
results  when  the  tests  have  been  scientifically  conducted. 
Especially  interesting  tests  have  been  made  by  Prof.  B.  F. 
Thomas*  in  1892,  and  Prof.  Ayrtonf  and  E.  A.  Medley  in  1894. 

*  B.  F.  Thomas ;  Transactions  American  Institute  of  Electrical  Engi- 
neers, 1892,  page  271. 

+  Philosophical  Magazine,  39,  1895,  page  389. 


COMPARISON   LIGHTS  187 

THE  INCANDESCENT  CARBON  FILAMENT  AS  A  PRIMARY 
STANDARD  OF  LIGHT 

193.  We  have  already  seen  an  attempt  made  to  employ 
incandescent  platinum  in  mass  or  in  foil  for  a  primary  stand- 
ard of  light.  As  early  as  1857  Zollner*  experimented  with 
incandescent  platinum  wires  for  the  purpose  of  studying  the 
light  radiation  from  them ;  but  these  studies  were  barren  of  any 
definite  photometrical  results.  Upon  the  advent  of  the  incan- 
descent lamp,  it  was  early  looked  upon  as  a  possible  light 
standard.  In  1885  a  committee  of  the  British  Association  f 
brought  forward  in  a  resolution  that,  "  a  unit  of  light  is  obtained 
from  a  straight  carbon  filament  at  right  angles  to  the  middle  of 
the  filament,  when  the  resistance  of  the  filament  is  one-half  of 
its  resistance  at  0°  Centigrade,  and  when  it  consumes  109  c.  g.  s. 
units  (100  watts)  of  electrical  energy  per  second."  It  was 
further  proposed  $  to  make  a  large  number  of  subjective  experi- 
ments on  human  eyes  to  obtain  a  coefficient  or  multiplying 
quantity  for  the  expression  of  the  illumination  from  the  stand- 
ard lamp,  by  the  change  in  the  resistance  of  the  filament.  In 
such  manner,  when  comparing  lights  or  sources  of  illumination, 
the  standard  filament  might  be  adjusted  until  the  spectrum 
curve  of  its  radiation  should  be  that  of  the  light  compared. 
Then  the  total  heat  and  light  radiations  of  the  illuminating 
source  and  the  standard  lamp  could  be  compared  at  equal 
distances  by  means  of  a  thermopile.  From  the  known  radiant 
properties  of  the  standard  lamp,  established  by  researches  on 
the  standard  filament,  the  compared  light  could  be  completely 
defined.  Abney§  had  already  proposed  the  definition  of  a 
standard  of  white  light  by  experimentally  establishing  formulas 
which  should  connect  the  radiation  from  the  filament  with  its 

*  PoggendorfP s  Annalen,  100, 1857,  pages  381  and  109  ;  1860,  page  256. 

t  British  Association  Report,  1885,  page  63. 

J  Reference  cited,  page  83. 

§  British  Association  Report,  1883,  page  422, 


188  PHOTOMETRIC AL   MEASUREMENTS 

energy,  current,  electromotive  force,  resistance,  and  temperature 
quantities.  He  proposed  the  adoption  of  a  standard  spectrum 
for  the  comparison  of  the  quality  of  lights,  the  quantity  to  be 
determined  photometrically. 

The  dimensions  of  the  carbon  filament  and  the  electrical 
quantities  involved  in  its  operation  are  all  capable  of  ready 
and  exact  determination.  It  would  thus  seem  to  be  admirably 
adapted  for  a  standard  light,  or  an  absolute  photometrical  stand- 
ard, in  the  sense  that  its  light  radiation  might  be  completely 
specified  by  reference  to  the  dimensions  of  the  filament  and  its 
temperature  of  operation.  Further,  such  a  standard  as  was 
pointed  out  in  the  British  Association  Report,  would  be  exceed- 
ingly flexible,  and  not  only  capable  of  adjustment  to  agree  in 
quality  with  the  compared  lights,  but  from  the  continuous 
nature  of  the  spectrum  of  carbon,  at  a  certain  temperature,  it 
would  conform  to  the  requirements  for  normal  quality  of  light. 
Certainly  no  source  of  illumination  as  yet  proposed  for  a  stand- 
ard light  has  so  many  obvious  advantages. 

The  failure  of  the  incandescent  lamp  to  fulfil  its  promise  of 
becoming  an  exact  standard  of  light  has  been  due  to  a  lack  of 
reproducibility  and  of  constancy  in  its  physical  character  when 
in  operation.  Though  it  would  seem  to  be  difficult  to  determine 
accurately  the  area  of  radiating  surface,  yet  doubtless  this  could 
be  accomplished  were  it  the  only  obstacle.  The  essential  dif- 
ficulty results  largely  from  the  tendency  of  carbon  to  assume 
an  allotropic  form  at  very  high  temperatures.  It  is  seemingly 
impossible  to  produce  homogeneous  carbon  filaments  or  to  flash 
filaments  until  the  surface  assumes  known  radiating  qualities. 

It  has  been  seen  that  the  presence  of  graphitic  carbon 
greatly  modifies  the  temperature  change  of  resistance,  so  that 
the  specification  of  a  certain  change  of  resistance  to  define 
the  temperature  is  not  feasible.  The  proposition  that  the 
operating  temperature  shall  be  defined  by  a  decrease  of  the 
resistance  to  one-half  of  its  value  at  0°  Centigrade,  loses  all 
certainty  through  the  lack  of  homogeneity  in  the  filament.  A 
further  difficulty  is  introduced  by  the  rapid  change  of  resist- 


COMPARISON  LIGHTS  189 

ance  due  to  hysteresis  and  the  slow  progressive  one  due  to 
molecular  readjustment. 

The  variation  in  the  eniissivity,  both  in  the  same  filament 
and  between  different  filaments  is  an  additional  uncertainty. 
Add  to  these  the  influence  of  the  blackening  of  the  chamber 
walls,  their  indefinite  absorption,  and  the  vaporization  of  the 
filament,  and  the  causes  for  the  failure  of  this  promising  stand- 
ard are  apparent.  The  failure,  briefly,  lies  in  the  inability  to 
establish  the  light  emitted  as  a  function  of  the  dimensions 
and  physical  properties  of  the  filament. 

THE  INCANDESCENT   LAMP  AS  A   COMPARISON  LIGHT 

194.  Before  the  advent  of  the  incandescent  lamp  in  a  per- 
fected commercial  form,  there  was  no  certainty  in  the  suc- 
cessively repeated  light  values  of  the  primary  and  comparison 
flames  then  used.  And  further,  the  light  strength  at  different 
times  during  any  one  burning  of  a  light  was  not  certainly 
comparable  in  a  series  of  values.  Attention  has  already  been 
called  to  this  in  a  previous  chapter,  and  the  opinion  was  there 
expressed  that  much  of  the  error  and  discrepancy  in  the  litera- 
ture of  photometrical  standards  and  tests  has  originated  from 
such  uncertainties. 

Though  the  incandescent  lamp  disappointed  those  who  an- 
ticipated finding  in  it  a  primary  standard  of  light,  principally 
from  the  failure  to  establish  a  constant  relation  between  the 
illuminating  power  and  defining  dimensions  and  physical  con- 
ditions, yet  the  incandescent  lamp  has  probably  been  of  greater 
service  photometrically  than  any  other  light  source.  This  ser- 
vice has  been  done  through  the  constancy  of  the  illuminating 
power  of  a  particular  filament  under  proper  conditions,  which 
has  made  possible  both  concordant  data  and  a  quantitative 
knowledge  of  the  variation  in  flame  standards. 

Among  the  first,  Preece*  in  1884  suggested  the  use  of  a 

*  Proceedings  Royal  Society,  Vol.  36,  1884,  page  272. 


190 


PHOTOMETRICAL   MEASUREMENTS 


small  incandescent  lamp  for  a  portable  photometer.  Later, 
the  reliability  of  this  light  as  a  secondary  standard  was  estab- 
lished by  Lummer  and  Brodhim.*  At  this  time  these  scientists 
were  engaged  in  an  investigation  of  light  standards,  especially 
of  the  amyl  acetate  lamp  and  flame.  Before  employing  the 
incandescent  lamp  as  a  reference  light,  they  carefully  studied 
its  photometrical  qualities.  The  colour  of  the  amyl  acetate 
flame  being  reddish,  the  colour  of  the  light  of  the  incan- 
descent lamp  was  accommodated  to  it  by  operating  the  lamps 
at  a  reduced  voltage.  Two  65-volt  lamps  were  operated  at  a 
constant  pressure  of  55  volts,  the  electricity  being  supplied  by 
a  storage  battery.  Of  the  two  lamps  so  tested,  one  styled  E 
was  burned  continuously,  while  the  other  one,  L,  was  operated 
at  certain  intervals.  They  were  compared  against  one  another 
at  frequent  .intervals,  being  placed  as  the  two  lights  on  the 
photometer  bar.  The  data  obtained  were :  — 


Hours  burned 

L 

Ratio  — 
K 

R 

L 

1 

1 

.8779 

20 

2 

.8764 

62 

3 

.8741 

154 

8.5 

.8724 

211 

13.5 

.8677 

In  these  tests  especial  accuracy  was  sought  in  the  measure- 
ment of  the  current  and  potential  of  the  lamps.  Under  their 
normal  conditions  of  burning,  the  light  energy  of  the  lamps 
varied  nearly  ten  times  as  rapidly  as  the  electrical  energy,  in 
consequence  an  error  of  .05  per  cent  in  the  measurement  of 
the  electrical  quantities  would  affect  the  light  strength  about 
.5  per  cent  at  normal  candle  power. 

The  conclusion  derived  from  these  tests  was  that  incandes- 


*  Zeitschrift  fur  Instrumentenkunde,  1890,  page  121. 


COMPARISON   LIGHTS  191 

cent  lamps  under  proper  electrical  conditions  proved  especially 
constant  light  sources.  In  addition  they  possess  two  excellent 
properties:  the  colour  of  their  light  may  be  adjusted  to  that 
of  the  compared  light,  and  they  are  portable  on  the  photom- 
eter bar  without  disturbance  of  their  illuminating  power. 

195 .  The  working  conditions  for  incandescent  lamps  employed 
as  secondary  photometrical  standards  have  been  fully  outlined 
in  the  discussion  of  the  physics  of  the  incandescent  lamp. 

When  employed  merely  for  the  purposes  of  comparison  there 
is  no  necessity  for  a  careful  determination  of  the  illuminating 
power.  Used  as  a  secondary  standard,  the  illuminating  power 
is  to  be  determined  by  reference  to  the  amyl  acetate  or  pentane 
flames,  the  proper  corrections  for  humidity,  etc.,  being  made. 
It  is  well  to  standardize  a  number  of  lamps,  reserving  one  or 
more  for  checking  lamps  in  more  frequent  use.  Obviously  it 
is  necessary  to  standardize  a  lamp  in  a  certain  marked  position 
with  reference  to  the  plane  of  the  photometer  screen,  and  in 
its  subsequent  use  this  relation,  once  selected,  is  to  be  main- 
tained in  all  cases. 

196.  Sensitiveness  in  measurement.  —  By  differentiating  the 
equations  between  the  illuminating  power,  and  the  energy,  cur- 
rent or  potential  (page  180),  the  rate  at  which  the  illuminat- 
ing power  changes  with  respect  to  any  one  of  these  variables, 
is  given.     Also,  by  referring  to  the  curves  for  these  relations 
(Fig.  48,  page  183),  the  change  in  illuminating  power  for  a 
given  change  in  any  one  of  the  electrical  quantities  may  be  im- 
mediately derived.     These  results  emphasize  the  need  for  very 
great  sensitiveness  as  well  as  accuracy  in  the  measurement  of 
the  electrical  quantities. 

197.  Precautions  are  needed  to  avoid  the  influence  of  tempo- 
rary set,  or  hysteresis  in  the  resistance  of  the  filament  (page 
175 ),  and  especially  the  permanent  set  due  to  abnormally  high 
voltage.     After  a  lamp  has  been  calibrated  it  should  not  have 


192  PHOTOMETRICAL  MEASUREMENTS 

a  pressure  impressed  upon  it  in  excess  of  the  voltage  at  which 
it  was  calibrated.  This  is  in  the  nature  of  a  general  observa- 
tion, for  in  particular  cases  it  may  be  found  desirable  to  cali- 
brate a  lamp  over  a  considerable  range  of  pressure,  and  plat  a 
curve  for  it  and  use  the  lamp  accordingly. 

Except  for  the  comparison  of  lights  of  reddish  tinge,  it  is 
not  necessary,  nor  is  it  even  desirable,  to  use  an  incandescent 
lamp  as  a  secondary  standard  at  any  temperature  short  of  that 
which  will  produce  a  clear  white  light.  A  carefully  selected 
lamp  will  usually  prove  as  constant  at  such  a  temperature  as 
when  operated  at  a  lower  temperature  and  emitting  a  reddish 
light. 

Further,  the  life  curves  show  that  new  incandescent  lamps, 
as  a  rule,  are  not  suitable  for  light  standards,  nor  do  they  be- 
come so  until  they  have  burned  a  sufficient  number  of  hours  to 
render  their  illuminating  power  practically  constant.  Gener- 
ally, after  burning  one  hundred  and  fifty  or  two  hundred  hours 
they  attain  this  desirable  stability. 

Overheated  lamps,  lamps  with  blackened  bulbs,  and  lamps 
with  rough  and  dull  black  filaments  are  not  suitable  for  photo- 
metrical  purposes.  Only  the  product  of  a  reliable  factory,  where 
careful  attention  is  paid  to  every  detail  of  manufacture  of  the 
filament,  and  thorough  exhaustion  of  the  chamber  is  accom- 
plished, should  be  selected.  The  filament  should  be  slowly 
flashed  and  present  a  smooth,  hard,  bright  gray  surface.  Lamps 
which  initially  burn  with  a  bluish  tinge  are  to  be  avoided; 
the  vacuum  in  such  cases  is  not  sufficiently  good  to  insure  the 
desired  constancy  in  the  filament. 

198.  The  advantages  of  the  incandescent  lamp  as  a  second- 
ary or  reference  standard  of  light  are,  briefly:  the  constancy 
of  the  illuminating  power  in  operation;  the  constancy  of  the 
illuminating  power  in  frequent  reproduction ;  freedom  from  the 
influence  of  atmospheric  conditions  so  disturbing  with  flames ; 
flexibility  in  accommodating  the  quality  of  the  light  over  a 
wide  range  from  the  reddish  tinge  of  many  flames  to  the  blu- 


COMPARISON   LIGHTS  193 

;sh  cast  of  the  arc  light ;  the  ability  to  produce  the  requisite 
quality  for  normal  white  light ;  its  cheapness,  convenience,  and 
simplicity;  and  finally,  the  accuracy  with  which  it  is  possible 
to  measure  and  control  the  electrical  quantities  involved  in  its 
operation. 

OIL   AND   GAS   LAMPS 

199.  Petroleum  burning  lamps.  —  In  1869  Rudorff*  employed 
as  a  comparison  light,  for  the  study  of  the  standard  candle,  an 
argand  burner,    with  the   usual  glass  chimney,  and  oil  as  a 
combustible.     Similar  lamps  were  employed  by  Siemens  and 
Hefner- Alteneck,  f  and  as  a  calibrated  reference  standard  in 
the  Edgerton  photometer.  $     In  this  latter  case  only  a  portion 
of  the  flame  was  used,  the  screening  being  accomplished  by  a 
movable  diaphragm,  somewhat  on  the  principle  of  the  Methven 
screen. 

A  petroleum  lamp  is  only  fairly  satisfactory  for  such  pur- 
poses ;  it  is  open  to  all  the  objections  urged  against  the  carcel 
lamp.  The  gradual  increase  in  flame  length,  the  charring  of 
the  wick,  and  fouling  of  the  chimney  render  frequent  calibra- 
tion of  the  flame  necessary.  Before  the  knowledge  of  flame 
standards  became  so  exact,  certain  early  experimenters  consid- 
ered such  lamps  to  be  convenient  and  reliable  for  purposes  of 
comparison. 

The  colour  of  the  flame  is  too  yellow  for  use  in  the  photom- 
etry of  incandescent  lamps.  In  contrast  with  the  superiority 
of  the  incandescent  lamp  for  such  uses,  the  petroleum  lamp  is 
both  uncleanly  and  unreliable. 

200.  The  keats  lamp.  —  This  is  an  English  form  of  the  carcel 
lamp,  burning  sperm  instead  of  colza-oil.     For  some  time  it 
was  thought  to  have  certain  advantages  as  a  primary  standard, 
but  was  soon  relinquished  for  this  purpose  and  employed  only 

*  Schilling's  Journal,  1869,  page  283. 
t  Elektrotech.  Zeitschrift,  1883,  page  454. 
|  Dingler's  Polytech.  Journal,  229,  page  48. 
o 


194  PHOTOMETRICAL  MEASUREMENTS 

as  a  comparison  light.  It  has  been  carefully  studied  by  W.  J. 
Dibdin.*  Its  properties  are  so  similar  to  those  of  the  carcel 
lamp  they  require  no  further  discussion. 

201.  The  benzine  lamp.f  —  Benzine,  uncombined  with  other 
combustibles,  has  been  used,  to  a  limited  extent,  in  simple  spirit 
lamps.     As  a  secondary  standard  it  has  proved  quite  constant 
and  reliable,  and  has  the  additional  merit  of  burning  with  a 
fairly  white  flame.     It  is  employed  in  such  a  capacity  in  the 
Leonhard  Weber  (page  81)  portable  photometer. 

202.  Argand  and  simple  jet  gas  flames.  $  —  These  lights  have 
been  frequently  discussed,  both  directly  and  indirectly,  espe- 
cially under  the  topics  of  the  Methven  screen  (page  126)  and  the 
pentane  lamp  (page  132).      Used  by  themselves,  or  in  con- 
nection with  a  screen,  they  are  fairly  reliable  reference  lights, 
and,  under  proper  conditions,  may  burn  with  steadiness,  though 
they  require  frequent  calibration. 

203.  Acetylene.  —  The  fitness  of  this  gas  for  furnishing  a  pri- 
mary standard  of  lighth  as  been  studied  to  some  extent.  §     No 
definite   results  have  been   accomplished,  and   no  conclusion 
regarding  its  photometrical  fitness  can  be  arrived  at  in  advance 
of  satisfactory  experimental  evidence.     Judging  from  the  ex- 
perience with  the  pentane  air-gas  standard,  the  design  of  a 
compact  and  portable  apparatus  will  prove  especially  difiicult. 
Another  difficulty  will  be  the  prevention  of  the  fouling  of  the 
burner. 

The  gas  burns  with  a  white  and  brilliant  flame,  whose  colour 

*  Journal  for  Gas  Lighting,  45,  1885,  pages  568  and  625;  also  consult 
Vol.  38,  1881,  page  719. 

t  Elektrotech.  Zeitschrift,  1883,  page  455. 

}  Consult  Journal  for  Gas  Lighting,  54,  1889,  page  968. 

§  Violle  ;  Comptes  Rendus,  112, 1896,  page  507  ;  and  June,  1899.  Also, 
"A  Study  of  the  Gas  Flame  from  Acetylene,"  L.  W.  Hartman,  Physical 
Review,  September,  1899,  page  176. 


COMPARISON   LIGHTS  195 

is  admirably  adapted  for  photometrical  purposes.  The  correc- 
tion factors  for  humidity  and  atmospheric  pressure  remain  to 
be  determined.  That  the  high  temperature  of  the  acetylene 
flame  would  indicate  that  the  correction  for  humidity  will 
prove  small,  does  not  follow:  for  the  amyl  acetate  flame  is  less 
affected  by  moisture  than  the  pentane  flame,  which  burns  at  a 
higher  temperature. 

Acetylene  being  a  simple  gas,  and  not  a  mixture,  can  be 
obtained  in  a  state  of  great  purity,  from  mineral  carbides,  and 
thus  meets  the  chemical  requirements  for  a  standard  combusti- 
ble. It  promises  to  become  an  open-flame  standard  of  great 
merit ;  but,  until  this  is  proven,  it  is  only  suitable  for  photo- 
metrical  work  in  the  capacity  of  a  comparison  light. 

At  the  present  time  a  number  of  investigations  are  in  prog- 
ress to  define  the  photometrical  properties  of  the  acetylene  flame 
for  use  as  a  primary  standard.*  In  the  physical  laboratory  of 
Cornell  University  such  investigations  are  being  accurately 
and  exhaustively  pursued,  and  their  conclusion  may  be  antici- 
pated to  define  the  chemical  and  illuminating  properties  of  the 
gas,  and  establish  the  necessary  correction  factors  for  its  flame. 
The  design  of  suitable  apparatus  and  an  appropriate  burner  are 
also  elements  in  these  investigations.  The  results  already  ob- 
tained are  of  a  promising  character,  and  justify  the  anticipation 
that  a  working  primary  standard  of  light  may  soon  be  devel- 
oped. 

*The  author  desires  to  express  his  obligations  to  Dr.  E.  L.  Nichols 
for  acquainting  him  with  the  experiments  he  is  conducting  and  granting 
permission  for  the  publication  of  this  note. 


CHAPTER  VI 

THE    PHOTOMETRY    OF    THE    INCANDESCENT    LAMP 

204.    The  light   distribution  from  an  incandescent  lamp  is  a 

function  of  the  shape  of  the  filament  (page  188),  and  this  will 
differ  amongst  lamps  to  the  extent  that  their  filaments  fail  of 
similarity  in  shape.  Such  statements  are  based  on  the  assump- 
tion that  the  intrinsic  brightness  of  the  incandescent  filament 
is  uniform  throughout  its  length,  which  is  practically  the  case 
if  they  have  been  properly  flashed. 

The  comparison  of  the  illuminating  power  of  incandescent 
lamps  is  very  generally  based,  and  exclusively  so  commercially, 
on  measurements  made  at  one  point  in  the  horizontal  plane. 
When  all  the  filaments  are  similarly  placed,  such  measurements 
have  a  certain  value;  but  these  data  can  only  refer  to  the 
luminous  intensity  in  that  particular  vectorial  direction,  and 
unless  factors  are  known  which  will  connect  the  intensity 
along  any  other  vector  with  that  measured,  such  single  values 
are  of  little  practical  or  theoretical  importance. 

Comparisons  of  illuminating  power  obtained  in  this  manner 
are  obviously  doubtful.  The  variations  in  the  shape  of  fila- 
ments are  so  marked  that  the  proper  comparison  of  their 
illuminating  power  follows  only  from  values  of  their  average 
spherical  light  distribution.  In  no  other  way  can  the  efficiency 
of  the  lamp  be  determined,  for  this  is  properly  a  ratio  between 
the  total  light  radiated  and  the  energy  transformed  in  the 
filament. 

Usually  the  illuminating  power  of  a  filament  is  graphically 
defined  by  five  curves,  giving  the  distribution  in  the  horizontal 
plane  and  in  four  vertical  circles  with  azimuths  of  0°,  45°,  90°, 

196 


PHOTOMETRY   OF   THE   INCANDESCENT   LAMP        197 


and  135°.     The  azimuth  is  reckoned  from  the  prime  meridian, 
which  is  defined  by  the  vertical  plane  through  the  photomet- 


rical  axis,  when  the  lamp  is  in  its  standard  or  marked  position, 
with  the  plane  of  the  filament  normal  to  the  photometrical 


FIG.  51. 

axis.     In  the  illustrations  a  curve  for  the  distribution  of  the 
light  in  a  vertical  plane  is  shown  in  Figure  50,  and  both  the 


198 


PHOTOMETRIC AL   MEASUREMENTS 


shape  and  position  of  the  filament  are  indicated ;  vwhile  the  dis- 
tribution in  the  horizontal  plane,  of  filaments  whose  shape  is 
sketched  in  each  case,  is  given  in  Figures  51  and  52. 


FIG.  52. 


The  intensity  at  the  tip  of  the  lamp  is  low,  because  the  area 
of  the  filament  projecting  in  this  direction  is  small ;  the  base 
entirely  screens  all  light  in  its  direction.* 


THE  PHOTOMETER  ROOM  AND  ITS  APPARATUS 

205.  The  size  of  the  room  in  case  no  flames  are  used  pho- 
tometrically is  of  little  consequence;  it  may  be  just  large 
enough  to  accommodate  the  apparatus  and  leave  space  for 
operating  it,  due  allowance  being  made  for  proper  ventilation. 
When,  as  must  be  the  case  in  most  laboratories,  flames  are 
photometered,  a  large  room  is  a  necessity  in  order  to  insure 

*  An  admirable  paper  by  Liebenthal  on  "  The  Light  Distribution  and 
the  Photometry  of  the  Incandescent  Lamp,"  may  be  found  in  Zeitschrift 
fur  Instrumentenkunde,  19,  1899,  pages  193  and  225. 


PHOTOMETRY   OF   THE   INCANDESCENT   LAMP        199 

uniform  conditions  of  the  aqueous  and  carbon  dioxide  contents 
of  the  air,  without  marked  drafts,  such  as  would  be  occasioned 
by  rapid  ventilation  in  a  small  room. 

For  the  general  practice  of  arc  and  incandescent  lamp  pho- 
tometry, a  suitable  room  would  have  its  dimensions  of  some 
twenty  feet  in  length  and  ten  feet  or  more  in  width,  and  would 
preferably  have  a  high  ceiling. 

The  room  should  be  entirely  darkened  when  measurements 
are  made.  To  this  end  outside  windows  should  be  permanently 
darkened  or  provided  with  inside  solid  wooden  shutters,  so 
fitted  that  no  light  will  leak  past  them.  It  is  well  to  vesti- 
bule the  doorway  leading  into  the  room,  as  is  frequently  done 
in  photographic  dark  rooms. 

All  surfaces  in  the  room  are  to  be  blackened  that  they  will 
absorb  all  light  falling  upon  them ;  and  all  the  light  reaching 
the  screen  should  be  radiated  directly  from  the  light  sources  or 
from  the  reflecting  mirrors,  and  not  from  irregularly  reflecting 
surfaces  about  the  room. 

The  walls  and  woodwork  may  be  painted  black,  employing  a 
paint  which  dries  with  a  dull  black  finish ;  for  a  bright  finish 
even  with  black  paint  would  make  a  partially  reflecting  surface ; 
or,  they  may  be  coated  with  a  black  wash.  This  wash  is  made 
with  fine,  clean  lampblack  and  glue  water. 

The  chairs,  tables,  and  other  furniture,  and  as  well,  all 
switches  and  fittings  should  be  finished  with  a  dull  black  sur- 
face. The  manufacturer  will  furnish  all  parts  of  the  photometer 
bench  thus  finished,  but  accessory  apparatus,  such  as  voltmeters, 
should  be  encased  in  black.  The  floor  is  often  neglected  after 
having  taken  the  most  elaborate  precautions  with  the  walls  and 
apparatus.  In  a  very  small  room  the  floor  may  be  left  un- 
painted,  but  unless  certain  that  no  light  can  be  reflected  from 
it  to  the  screen,  it  is  advisable  to  coat  the  floor  with  a  black 
stain. 

The  judgment  in  individual  cases  will  indicate  how  far  to 
carry  out  these  precautions,  provided  it  is  based  on  experience. 

Such,  elaborate  attention  to  the  prevention  of  reflection  of 


200 


PHOTOMETRICAL  MEASUREMENTS 


light  would  also  suggest  that  the  pains  be  taken  not  to  place 
white  paper  or  other  like  objects  where  they  may  act  as 
reflectors. 

206.  The  photometer  bench  is  usually  mounted  on  a  firm, 
heavy  table,  especially  looking  toward  the  protection  of  flames 
from  mechanical  disturbances.     The  operating  side  of  the  bench 
is  placed  quite  close  to  the  edge  of  the  table,  though  it  is  con- 
venient to  have  the  table  considerably  wider  than  the  bench,  to 
accommodate  instruments,  rheostats,  and  other  accessories. 

207.  A  permanently  wired  table  is  advisable.     The  wiring 
should  provide  connections  for  a  working  incandescent  lamp  at 
each  end  of  the  bench,  and  a  small  reading  lamp  to  be  placed 


FIG.  53. 

on  the  screen  carriage.  Attachments  for  a  voltmeter  should  be 
provided  for  each  working  lamp,  as  close  as  possible  to  the 
terminals  of  the  lamp.  It  is  also  convenient  to  place  a  switch 
at  the  centre  of  the  table  and  within  easy  reach  of  the  operator 
for  each  of  the  three  lamps.  Connections  should  also  be  left 
in  each  main  lamp  circuit  for  the  regulating  rheostats.  A 
plan  for  wiring  is  shown  in  Figure  53,  which  necessitates  but 
one  voltmeter. 

208.  A  reading  lamp  attached  to  the  carriage  carrying  the 
screen  will  prove  a  great  convenience.  This  lamp  should  be  of 
low  light  power  so  as  not  to  affect  the  eyes  of  the  observer.  A 


PHOTOMETRY  OF  THE   INCANDESCENT  LAMP        201 

lamp  with  a  cylindrical  bulb  may  be  used,  and  this  is  to  be 
fitted  with  a  metal  reflector,  to  throw  the  light  on  the  scale  bar, 
and  at  the  same  time  shade  the  observer's  eyes  from  the  direct 
light.  The  lamp  is  only  lighted  when  a  reading  is  made. 

209.  A  canopy  of  some  description  should  be  arranged  to 
shield  the  operator's  eyes  from  the  lights  under  comparison. 
Black  plush,  or  velvet,  is  a  suitable  light-proof  material  for 
such  a  canopy,  and  it  may  be  attached  to  a  wire  frame  which  is 
either  fastened  to  the  screen  carriage  or  to  some  special  carriage 
which  shall  be  moved  by  that  carrying  the  screen.     The  frame 
if  too  large  would  limit  the  travel  of  the  screen.    The  canopy 
should  entirely  surround  the  screen  and  have  lateral  openings 
in  the  photometer  axis  slightly  larger  than  the  openings  in  the 
screen  box ;  but  at  no  position  on  the  bar  should  the  canopy  cut 
off  light  from  the  screen. 

Some  photometricians  prefer  to  screen  the  comparison  lights 
with  canopies.  This  is  a  matter  of  no  consequence  when 
incandescent  lamps  are  used,  but  with  open  flames  a  canopy 
enclosing  them  is  objectionable,  as  it  interferes  with  the 
adjustment  of  the  flame,  and  by  even  partially  confining  it, 
may  alter  its  value  (page  121). 

In  some  instances  wooden  canopies  are  built  about  the 
lamps,  and  small  pieces  of  coloured  glass  are  inserted  for  view- 
ing the  lights.  The  use  of  all  coloured  glass  in  photometrical 
practice  is  to  be  avoided,  as  it  gives  a  persistent  colour  cast  to 
the  eye,  which  may  introduce  an  error  when  adjusting  the 
screen.  Coloured  glass  is  needed  for  viewing  the  electric  arc, 
but  this  should  never  devolve  upon  the  observer  at  the  screen. 

210.  The  rheostats  used  with  the  incandescent  lamps  should 
afford  very  close  adjustment  of  the  voltage  over  a  considerable 
range.     This  is  accomplished  by  using  two  rheostats  with  each 
lamp.     Each  rheostat  should  have  numerous  steps,  the   one 
with  a  high  resistance  to  the  step  and  the  second  with  very 


202  PSOTOMETRICAL  MEASUREMENTS 

low  resistance  intervals,  but  having  a  total  resistance  slightly 
in  excess  of  the  resistance  interval  of  the  first  rheostat.  This 
will  insure  sufficiently  sensitive  adjustment.  Circular  enamel 
rheostats  are  well  adapted  for  this  work. 

211.  The  source  of  electromotive  force  for  incandescent  lamp 
photometry  should  be  the  storage  battery.     The  illuminating 
power   of   the   incandescent   lamp   is   so   sensitive  to   slight 
changes  in  voltage,  that   a  very  constant  source  of   electro- 
motive force  is  needed  in  its  photometry.     A  very  steadily- 
running  dynamo  may  answer  fairly  well,  provided  it  supplies 
current  only  to  the  photometer  room.     Though  a  battery  of 
even  small  cells  will  be  the  most  expensive  item  in  the  equip- 
ment of  the  photometer  room,  its   installation   is   advisable 
when  accurate  work  is  attempted. 

212.  The  sensitiveness  of  the  voltmeter  and  the  ammeter. — 
From  the  discussion  of  the  illuminating  power  as  a  function 
of  the  volts,  amperes,  or  watts  (page  180),  and  an  inspection 
of  their  graphical  relations  (Fig.  48),  the  necessity  for  great 
sensitiveness  in  the  instruments  measuring  these  quantities, 
and  for  the  accurate  calibration  of  their  scales,  is  seen. 

Careful  attention  to  these  details  is  imperative;  but  the 
photometrician  should  not  be  content  with  generalizations  in 
such  matters,  but  be  able  to  subject  them  to  specific  calcula- 
tion. 

Where  such  great  sensitiveness  and  high  accuracy  are 
needed,  the  calibration  should  not  be  left  wholly  with  the 
manufacturer  of  the  instruments,  but  be  carefully  verified 
by  the  photometrician  himself ;  and  this  should  be  done  fre- 
quently to  insure  confidence  in  the  accuracy  of  the  scale  read- 
ings. The  potentiometer  method  is  especially  recommended 
for  the  calibration  of  both  the  voltmeter  and  the  ammeter, 
being  accurate  and  readily  applied.* 

*  "  Electrical  Measurements,"  Carhart  and  Patterson,  p.  206. 


PHOTOMETRY   OF   THE  INCANDESCENT   LAMP        203 

213.  A  calculation  of  sensitiveness.  —  The  data  for  this  calcu- 
lation are  obtained  from  the  table  on  page  182,  corresponding 
to  the  curves  of  Figure  48. 

The  equation  between  the  candle  power  and  the  volts  is 
(page  181) 

P=aVx.  (7$  bis) 

To  find  the  value  of  the  exponent  x  the  equation  is  given 
the  logarithmic  form  twice,  — 

log.  P!  =  log.  a  +  x  log.  Fi.  | 
log.  P2  =  log.  a  +  x  log.  F2.  ) 

From  these  equations  by  elimination  of  log.  a, 

(84) 


For  the  solution  of  the  equation,  observed  values  are  taken, 
which  are  characteristic  and  sufficiently  wide  apart.  From  the 
table  are  selected,  VJ  =  115 ;  Pl  =  32.7 ;  F2  =  95,  and  P2  =  11.05, 
from  which  by  substitution  in  equation  84, 

a?  =  5.7. 

Similarly  between  the  observations  at  85  and  105  volts, 

x  =  5.9, 
and  between  101  and  109  volts, 

x  =  5.78. 

Taking  5.8  as  a  working  value  for  x,  the  equation  reads 
P=aF58.  (85) 

For  the  purpose  in  hand,  the  constant  a  will  be  calculated  for 
104  volts  and  18.8  candle  power,  and  the  value  is  found  to  be, 

a  =  37xlO~14. 


204  PHOTOMETRICAL  MEASUREMENTS 

The  general  equation  for  this  particular  lamp  is  now  com- 
pletely known,  and  is 

P  =  37xlO-14F5-8.  (86) 

214.  The  potential  sensitiveness  of  the  candle  power,  or  the 
candle-power-voltage  rate  of  change  is  found  by  differentiating 
equation  86.  Then 

^  =  (5.8  x  37  x  10  - 14)  F4-8,  (87) 

tt  V 

from  which  a  curve  of  sensitiveness  can  readily  be  calculated 
and  platted. 

A  particular  value  of  the  sensitiveness  will  be  sought  for  104 
volts  and  18.8  candles,  in  order  to  find  the  change  in  volts  to 
produce  a  change  of  the  one-hundredth  part  in  the  illuminating 
power.  This  is  found  by  solving  for  AF,  AP  being  taken  at 
0.188. 

AF=  °'188 


5.8  x  37  x  10-14  x  10448 
which  yields 

A F=  0.18  volts. 

215.  The  application  of  these  results  shows  conclusively  the 
necessity  for  a  sensitive  and  accurately  calibrated  voltmeter, 
for  the  scale  must  be  read  to  0.18  volt  with  certainty,  for  an 
error-limit  as  great  as  one  per  cent  in  the  illuminating  power. 

The  sensitiveness  required  in  the  ammeter  or  wattmeter,  if 
one  is  used,  can  be  calculated  in  a  similar  manner. 

216.  Adjustable  lamp  holders.  — The  complete  photometrical 
study  of  the  incandescent  lamp  will  include  the  distribution 
of  its  light  in  the  horizontal  or  equatorial  plane,  and  in  certain 
of  the  meridian  planes  of  the  filament;  thus  the  spherical 
distribution  of  light  may  be  arrived  at  when  a  large  number 
of  properly  disposed  measurements  have  been  made,  the  dis- 
tribution being  referred  to  the  optical  centre  of  the  filament. 
These  are  the  conditions  governing  the  design  of  any  device 


PHOTOMETRY   OF   THE   INCANDESCENT   LAMP        205 

for  holding  the  lamp  in  the  proper  positions  for  such  measure- 
ments;  or,  geometrically,  the  lamp  must  be  capable  of  the 
angular  adjustment  of  its  position  in  both  the  azimuth  and 
meridian  planes,  with  ref- 
erence to  the  optical  centre 
of  the  filament.     The  de- 
vice   for    meeting    these 
conditions   is   so   readily 
apparent  and    so   simple 
that  practically  all  holders 
are  of  one  type. 

Amongst  the  earliest 
forms  of  the  device  was 
the  lamp  holder  used  in 
the  Franklin  Institute 
tests.*  Later  this  was 
given  its  present  form  by 
C.  Heim,t  (Fig.  54). 

As  such  holders  are 
now  made,  the  lamp  is 
carried  by  a  vertical 
spindle  bearing  a  cir- 
cularly divided  azimuth 
scale,  and  furnished  with 
a  clamp  for  setting  the 
lamp  in  any  desired  azi-  FIG.  54. 

muth.     This  arrangement 

is  borne  either  by  a  yoke,  or  by  a  curved  arm  pivoted  to  move 
in  a  plane  at  right  angles  to  the  azimuth  plane,  or  in  a  meridian 
plane,  and  which  may  be  firmly  clamped  in  position  about  a 
second  circularly  divided  scale  which  indicates  the  angular 
inclination  of  the  equatorial  plane  of  the  lamp  to  the  horizontal. 


*  Keport  on  the  Efficiency  and  Duration  of  Incandescent  Electric 
Lamps,  Franklin  Institute,  1885,  page  14. 

t  Elektrotech.  Zeitschrift,  1886,  page  384  ;  also  1887,  page  358. 


206 


PHOTOMETRICAL   MEASUREMENTS 


The  spindle  carrying  the  incandescent  lamp  is  adjustable 
vertically  so  as  to  bring  the  optical  centre  of  the  filament  in 
the  axis  of  the  curved  arm ;  and  when  the  lamp  is  placed  in 
the  holder  it  must  be  adjusted  accurately  to  meet  this  condi- 
tion. 


217.   Rotating  lamp  holders.  —  The  spinning  of  the  filament 
is  readily  accomplished  by  slightly  modifying  such  a  holder. 

The  pivot  of  the  curved 
arm  is  hollowed  to 
receive  a  spindle  carry- 
ing two  small  pulleys. 
A  light  belt  passes  from 
the  inner  pulley,  and  is 
deflected  by  two  idle 
pulleys  placed  at  the 
bend  of  the  arm,  and 
then  passes  around  a 
fourth  pulley  on  the 
lamp  axis  of  the  holder, 
which  in  this  case  be- 
comes a  light  vertical 
shaft.  The  outer  pulley 
on  the  horizontal  shaft 
is  belted  to  a  small  elec- 
tric motor  for  driving 
the  arrangement. 

The  lamp  spindle 
carries  slip  rings  for 
maintaining  the  electri- 
cal current.  A  rigid 
device  for  clamping  the 
FIG.  55.  curved  arm  in  any  de- 

sired position  completes 

the   apparatus.      A  rotator   recently   designed  by  Elmer   G. 
Willyoung  (Fig.  55)  has  an  additional  pair  of  brushes  for  the 


PHOTOMETRY  OF  THE  INCANDESCENT  LAMP    207 

voltmeter  terminals,  so  that  the  potential  difference  at  the 
lamp  itself  may  be  measured,  thus  avoiding  the  drop  of  poten- 
tial over  the  main  contacts. 

The  essentials  of  such  an  apparatus  are  solidity  of  all  its 
parts  and  excellent  balance,  that  it  may  operate  at  a  high 
speed  without  vibration. 

218.  The  proper  working  length  of  the  photometer  bar  is  a 

matter  to  be  determined  in  individual  cases,  depending  upon 
the  size  of  the  lamps  photometered  and  the  degree  of  sensitive- 
ness desired  in  the  measurements.  The  maximum  sensitive- 
ness with  any  bar  occurs  when  the  screen  is  in  balance  midway 
of  the  lights  compared.  In  general,  for  any  setting  increased 
sensitiveness  follows  an  increase  of  the  distance  between  the 
compared  lights. 

In  the  photometry  of  incandescent  lamps  of  ordinary  illumi- 
nating power,  a  working  distance  between  the  compared  lamps 
of  100  centimetres  may  be  used,  but  a  distance  of  150  or  200 
centimetres  is  to  be  preferred.  Probably  the  most  generally 
useful  and  the  advisable  free  length  of  the  bar  is  250  centi- 
metres, or  100  inches. 

219.  The  graduation  of  the  bar.  —  Two  classes  of  scales  may 
be  engraved  on  the  bars :  one  is  the  equally  divided  scale, 
while  the  other  is  a  proportional  one.     Each  millimetre  divi- 
sion of  the  metric  scale  should  be  engraved ;  and  when  the  bar 
is  divided  into  inches  each  tenth-inch  only  need  be  engraved, 
as  smaller  divisions  can  readily  be  estimated. 

220.  The  proportional  scales  are  based  on  the  general  photo- 
metrical  law: 

fr       A2 

(88) 

I  being  the  distance  from  the  standard  whose  intensity  is  Is  to 
the  screen.  A  proportional  scale  will  enable  the  intensity  /c  of 
the  compared  light  to  be  read  directly  from  the  scale,  provided 
it  has  been  adjusted  to  a  certain  value  for  /,. 


208  PHOTOMETKICAL   MEASUREMENTS 

221.  The  calculation  of  proportional  scales.  —  Some  imported 
photometers  have,  in  addition  to  a  metric  scale,  a  proportional 
one  from  which  German  candle  power  (Kerzeii)  may  be  read 
directly  when  the  amyl  acetate  standard  is  used.  In  this  case, 
/,  =  0.833,  being  taken,  a  few  properly  selected  values  for  Ie 
may  be  assumed  and  the  equation 


Jc  =  0.833  v    ~  ;  (89) 

then  solved  for  the  corresponding  values  of  I.  From  these 
values  a  curve  may  be  platted,  and  from  the  curve  the  entire 
scale  may  be  laid  out. 

Confining  the  discussion  to  ordinary  practice  with  a  standard 
incandescent  lamp,  it  is  clear  that  a  permanent  proportional 
scale,  engraved  on  the  bar,  will  require  the  readings  to  be 

multiplied  by  a  factor,  the  ratio  — f  in  case  a  standard  lamp  of 

intensity  /",  is  used  when  the  scale  was  designed  for  direct 
reading  with  a  standard  of  the  value  I'8. 

A  very  satisfactory  method  avoids  the  use  of  a  permanently 
marked  proportional  scale  for  a  temporary  one  based  on  the 
value  of  the  standard  lamp  in  use  at  the  time.  This  may  be 
calculated  entirely,  or  may  be  marked  by  the  graphical  method 
just  given. 

A  hard-wood  bar  may  be  attached  to  the  rail  with  a  strip  of 
paper  fastened  on  it,  which  can  then  be  directly  marked 
off  from  the  graduated  scale  to  conform  with  the  divisions 
calculated.  By  attaching  an  auxiliary  index  finger  to  the 
travelling  carriage  both  scales  may  be  read  simultaneously. 

A  second  variety  of  proportional  scales,  the  ratio  scale,  may 
prove  convenient.  This  is  based  on  serial  values  for  the  ratio 
of  two  lights.  It  is  calculated  by  solving  equation  88  for  I. 
Writing 

|  =  P  (90) 


PHOTOMETRY   OF   THE   INCANDESCENT  LAMP        209 
and  substituting  this  in  the  equation, 

VPl  =  L-l  (91) 

and 

l=— ^ (92) 

VP+1 

From  the  table  (Appendix  C,)  a  corresponding  value  for  the 
distance  I  is  obtained  for  each  serial  value  of  P,  and  the  scale 
marked  off  accordingly.  This  table  is  based  on  a  length  L  of 
100  units ;  for  any  other  length,  aL,  the  scale  distance  would 
be  al,  for 

al  =  —^- —  (93) 

VP  +  I 

The  value  of  Ic  in  terms  of  the  unit  It  is  thus  * 

/C  =  P/,  (94) 

THE  PKACTICE  OF  THE  PHOTOMETRY  OF  THE 
INCANDESCENT  LAMP 

222.  Adjusting  the  screen.  —  Merely  moving  the  screen  slowly 
along  the  track  until  equilibrium  of  the  two  illuminations  is 
apparently  obtained,  is  a  practice  to  be  avoided.  The  eye  is 
thus  gradually  led  up  to  a  condition  that  produces  both  fatigue 
and  uncertainty ;  nor  will  it  suffice  to  perform  the  operation 
more  rapidly.  The  screen  should  be  brought  quickly  to  a 
position  of  approximate  equilibrium  of  the  illuminations,  and 
then  moved  slowly  both  to  the  right  and  to  the  left,  un^il  a 
clearly  observed  difference  of  the  illuminations  is  noted.  These 
contrasts  both  sharpen  and  rest  the  eyesight,  and  the  screen 
can  then  be  moved  to  the  balanced  position  with  certainty.  It 
is  advisable  to  test  the  setting  further  by  moving  the  screen  to 
the  right,  say,  until  the  slightest  clearly  perceived  difference 
in  the  illuminations  is  found,  noting  the  scale  reading  at  this 
point  and  repeating  the  process  to  the  left.  Placing  the  screen 

*  See  table  Appendix  C,  for  value  of  P. 

p 


210  PHOTOMETRICAL  MEASUREMENTS 

now  midway  between  the  settings,  if  the  illuminations  are 
found  to  be  in  balance,  this  setting  may  be  finally  taken  with 
confidence.  This  process  of  justification  can  only  be  readily 
applied  with  an  equably  divided  scale,  though  with  other 
scales  the  screen  is  to  be  brought  to  equilibrium  through  a 
slight  movement  in  each  direction. 

To  find  the  value*  through  which  the  illumination  of  the 
screen  changes,  suppose  the  screen  is  at  a  distance  I  from  a 
light  of  such  intensity  that  the  screen  will  receive  P  units  of 
illumination  at  the  unit  distance  from  it.  The  illumination  / 
at  the  distance  I  is 

1=  f,  (95) 

and  the  change  of  the  illumination  A/,  through  a  small  move- 
ment AZ  in  adjusting  the  screen  is,  the  distance  from  the  light 
now  being  I  -f-  A?, 

AI=£*(nfV     '          (96) 

These  somewhat  tedious  methods  are  especially  advised  for 
those  beginning  photometrical  work.  Skill  in  such  details  is 
readily  acquired,  and  in  a  short  time  settings  can  be  rapidly 
made. 

223.  The  personal  factor  originates  in  the  part  which  the 
judgment  plays,  making  the  settings  of  the  screen  ultimately 
dependent  upon  a  state  of  the  optic  nerve  tract.  The  difficul- 
ties here  are  of  the  same  character  as  those  confronted  when 
the  standards  of  illumination  were  considered. 

It  is  interesting  to  note  some  relevant  experiments  with  the 
Bunsen  screen  made  by  E.  L.  Nichols. f  These  were  devoted 
to  comparisons  between  two  incandescent  lamps  supplied  by  a 
storage  battery,  which,  both  by  selection  of  the  lamps  and 

*  Philosophical  Magazine,  36,  1893,  page  122. 

f  Transactions  American  Institute  of  Electrical  Engineers,  6,   1889, 


PHOTOMETRY   OF   THE  INCANDESCENT   LAMP        211 

their  adjustment,  were  brought  to  practical  equality  of  colour 
and  intensity  of  illumination.  The  sight  box  seems  to  have 
been  partitioned  so  that  each  eye  was  independently  busied 
with  its  respective  side  of  the  screen.  Series  of  observations 
were  made  independently,  and  under  similar  conditions,  by  two 
practised  observers.  These  observations  wandered  from  a 
certain  established  value  by  a  mean  of  nearly  1.008,  though  in 
some  cases  the  departure  from  the  fixed  value  greatly  exceeded 
this  amount. 

When  one  eye  alone  was  brought  to  view  both  sides  of  the 
screen  simultaneously,  the  departure  was  reduced  to  about 
1.003,  and  it  was  indifferent  whether  the  right  or  left  eye  was 
used. 

As  will  be  seen,  this  departure  falls  mainly  to  one  side  or 
other  of  the  normal  point,  depending  upon  an  idiosyncrasy  of 
the  observer.  Some  physicists  have  assumed  this  departure  to 
be  somewhat  constant,  both  in  amount  and  direction,  and  that 
it  may  be  determined  individually  by  the  observer  and  applied 
as  a  correction  factor  to  his  observations. 

Prior  to  this  Liebenthal*  had  already  investigated  this 
factor  with  the  added  complication  of  the  change  in  the  screen 
itself.  The  mean  value  which  he  gives  for  a  correction  factor, 
in  the  observations  he  is  discussing,  is  1.002 ;  but  this  varied 
from  time  to  time  with  changes  in  the  screen  and  in  the  state 
of  the  eye.  Seemingly  the  quantitative  discussion  of  the  per- 
sonal discrepancy  of  observations  should  be  regarded  as  valu- 
able for  illustration  rather  than  practice. 

In  case  both  eyes  are  used  independently  in  the  reading  of  a 
Bunsen  screen,  the  mind  is  compelled  to  balance  two  judg- 
ments, arrived  at  from  independent  data;  hence  arises  the 
uncertainty.  In  an  observation  the  effect  produced  through 
the  right  eye  may  unconsciously  preponderate,  while  in  the 
very  next  observation,  it  may  be  the  left  eye;  and  this  is  fur- 
ther determined  by  the  relative  fatigue  of  the  eyes.  As  a  rule 

*  Elektrotech.  Zeitschrift,  1888,  page  102. 


212  PHOTOMETRIC AL   MEASUREMENTS 

the  colour  sensitiveness  differs  in  the  individual  in  kind  and  de- 
gree between  the  eyes  ;  and  except  in  rare  cases,  where  identical 
conditions  confront  each  eye,  binocular  observations  should  be 
avoided.  Even  should  the  screen  be  so  arranged  that  the  eye 
may  view  both  sides  of  it  coordinately,  the  setting  will  be  the 
result  of  a  compromised  judgment,  and  be  uncertain  to  that 
extent.  All  this  emphasizes  the  advisability  of  monocular 
readings,  so  that  the  personal  factor  may  be  more  consistent. 

With  an  apparatus  such  as  the  Lummer-Brodhun  contrast 
optical  screen,  which  is  monocular,  the  discrepancy  between 
individual  observers  may  be  considerable,  and  the  personal 
factor  seems  to  vary  greatly  from  time  to  time. 

It  is  clearly  seen  that  a  real  difficulty  in  photometrical  prac- 
tice is  here  confronted. 

Since  the  intensity  and  colour  sensitiveness  of  the  eye  differs 
generally  to  some  extent  in  the  individual  observer,  but  to  a 
greater  extent  between  different  observers,  in  case  the  lights 
compared  are  of  dissimilar  colour  the  matter  of  personal  drift  in 
the  settings  will  be  more  thoroughly  emphasized,  while  it 
attains  its  least  significance  when  lights  of  similar  quality  are 
compared.  All  this  adds  renewed  emphasis  to  the  assertion 
that  photometry  is  only  possible  between  similar  qualities  of 
light,  compared  under  conditions  of  equal  illumination  of  the 
sides  of  the  screen. 

224.  The  fatigue  of  the  eye. — Through  the  continued  action  of 
daylight  on  the  retina,  the  eye  falls  into  a  condition  of  minimum 
sensitiveness  toward  gradations  of  light,  but  recovery  is  rapid 
in  the  dark.  The  best  photometrical  results  are  obtained  when 
an  operator  is  assigned  to  the  adjustment  of  the  screen  alone, 
leaving  the  manipulations  of  the  lamps  to  another.  The  ob- 
server, on  entering  the  photometer  room,  should  remain  in 
darkness  for  some  minutes  before  attempting  the  reading  of 
the  screen,  and  should  not  keep  his  eyes  continuously  at  work 
on  the  illuminated  screen.  After  looking  at  this  for  a  time,  a 
coloured  cast  seems  to  flash  over  it,  or  it  becomes  bordered 


PHOTOMETRY   OF   THE  INCANDESCENT   LAMP        213 

with  grayish  light.  These  are  complementary  fatigue  phe- 
nomena (page  17),  and  warn  the  operator  to  rest  the  eyes. 

225.  Photometrical  skill  is  soon  acquired  by  the  operator,  and 
through  patience  and  careful  training  he  will  attain  rapidity 
and  accuracy  in  his  work.     Photometry  is  no  exception  in  this 
regard,  that  results  obtained  by  experienced  observers  are  alone 
to  be  credited.     Though  the  matter  of  the  comparison  of  equal 
illuminations  seems  so  simple  an  act  that  even  an  inexperienced 
eye  should  accomplish  it  with  satisfactory  accuracy,  the  causes 
leading  to  the  personal  factor  make  it  far  otherwise.     Even 
with  a  considerable  degree  of  experience  the  opportunities  are 
numerous  for  errors  of  judgment  and  observation,  and  for 
omissions. 

226.  The  precautions  in  the  use  of  flame  standards  have  already 
been  pointed  out  (page  159),  and  are  to  be  observed  in  case  the 
photometry   of  the   incandescent  lamp   begins   with   such   a 
standard.      One  who  has   not  attained   considerable   experi- 
mental skill  with  the  use  of  flames  can  not  expect  to  obtain 
any  degree  of  accuracy  with  these  standards.    Unless  one  can 
bring  time,  patience,  and  a  clear  grasp  of  the  subject  to  the 
task,  it  is  advisable  not  to  attempt  the  use  of  such  standards, 
but  to  employ  reliably  calibrated  incandescent  lamps,   thus 
greatly  simplifying  such  measurements,  and  insuring  a  certain 
degree  of  accuracy  from  the  first. 

227.  Precautions  in  the  use  of  incandescent  lamp  standards.  — 

Aside  from  the  necessity  for  a  close  adjustment  of  the  voltage 
and  care  to  be  exercised  not  to  exceed  the  voltage  for  which 
lamps  have  been  calibrated,  there  are  a  few  significant  minor 
details. 

The  bulbs  must  be  thoroughly  cleaned,  preferably  with  a 
dilute  solution  of  alcohol  or  ammonia.  A  standard  lamp 
should  be  calibrated  in  a  marked  position,  and  replaced  in  the 
photometer  in  a  like  position.  It  is  well  not  to  calibrate  a 
filament  placed  with  its  edge  toward  the  screen,  but  rather  to 


214  PHOTOMETRICAL  MEASUREMENTS 

place  the  plane  of  the  filament  at  right  angles  with  the  pho 
tometrical  axis. 

Both  lamps  compared  must  be  carefully  centred  with  respect 
to  this  axis.  This  is  readily  accomplished  by  running  the 
screen  up  to  each  lamp  in  turn,  and  adjusting  the  height  so 
as  to  bring  the  optical  centre  of  the  filament  to  lie  in  the  pho- 
tometrical  axis.  The  same  observation  applies  to  centring  a 
standard  flame. 

The  location  of  the  optical  axis  of  any  given  filament  must 
be  an  act  of  judgment  unless  a  meridian  curve  of  the  light 
distribution  from  the  filament  is  at  hand.  In  the  plain  horse- 
shoe filament  this  lies  just  above  the  centre  of  its  figure,  while 
if  the  filament  is  looped,  it  is  somewhat  higher.  This  matter 
does  not  call  for  extreme  accuracy. 

Another  observation  will  bear  repeating  in  this  connection : 
after  a  standard  lamp  has  been  obtained,  two  or  more  appro- 
priate lamps  should  be  selected  and  accurately  compared  with 
it,  the  lamps  in  each  case  being  brought  to  a  like  quality  of 
light  with  the  standard.  These  are  then  to  be  placed  aside  to 
serve  as  checks  for  the  standard. 

Ordinarily  the  standard  lamp  should  not  be  operated  through 
a  great  range  of  incandescence,  even  should  its  constant  be 
known,  and  the  characteristic  curves  accurately  determined ; 
with  such  care  the  useful  life  of  the  lamp  will  be  prolonged, 
and  the  quality  of  the  light  will  be  more  nearly  constant. 
Eather  obtain  a  working  range  by  the  use  of  a  number  of 
lamps,  of  graded  illuminating  powers,  or  voltages,  or  a  com- 
bination of  these.  Then  the  characteristics  for  these  lamps 
over  a  limited  range  can  be  determined  from  one  standard. 

When  a  standard  lamp  is  used  on  the  photometer,  it  should 
be  kept  incandescent  only  when  needed  for  a  measurement; 
between  such  events  the  current  should  be  turned  off. 

A  small  matter,  but  one  that  may  assume  importance,  is  that 
all  labels  should  be  attached  before  the  lamp  is  photometered, 
even  though  they  be  small  ones,  and  placed  at  the  base  next 
the  cap. 


PHOTOMETRY   OF   THE   INCANDESCENT   LAMP        215 

228.  Spinning  the  lamp.  —  This  process  may  be  applied  to  a 
lamp  when  photometered,  provided  a  suitable  rotator  is  avail- 
able, otherwise  it  is  apt  to  lead  to  erroneous  results. 

The  speed  at  which  the  lamp  is  to  be  rotated  will  depend  on 
certain  conditions.  A  speed  of  two  turns  *  per  second  has  been 
prescribed,  but  this  is  too  low,  while  a  speed  of  three  turns  per 
second  is  also  in  current  use.  A  speed  of  six  turns  per  second, 
if  the  filament  will  bear  it,  is  advised.  The  proper  speed  is 
not  the  same  for  all  observers.  This  may  be  approximated  in 
a  given  case  by  fastening  two  pieces  of  dark  paper  on  the  lamp 
bulb  with  rubber  bands,  the  pieces  to  be  placed  opposite  each 
other,  and  to  be  of  such  size  as  will  sensibly  diminish  the  light 
falling  on  the  screen  when  they  are  facing  it.  If  the  lamp  is 
now  rotated  until  the  light  falling  on  the  screen  ceases  to  flicker, 
the  critical  speed  has  been  found.  But  many  filaments  will  not 
admit  of  such  speed  for  any  length  of  time.  Looped  filaments, 
especially  if  very  long  and  slender,  are  difficult  to  spin ;  the  fila- 
ment best  adapted  for  this  process  is  the  stiff  horseshoe  type. 

The  process  can  be  applied  to  many  filaments  at  moderate 
incandescence,  but  if  this  is  increased  until  the  temperature 
approaches  the  plastic  state  of  the  carbon,  the  filament  will  be 
markedly  deformed.  If  the  filament,  too,  is  poorly  centred,  it 
will  be  apt  to  break  at  a  high  speed.  The  tangential  force  may 
cause  a  filament  to  spread  until  it  touches  and  breaks  the  bulb. 
In  any  case  the  filament  must  be  closely  watched  to  note 
whether  it  is  especially  deformed  by  the  spinning.  If  this  is 
the  case  the  spherical  distribution  of  the  light  is  correspondingly 
affected,  and  measurements  made  when  the  filament  is  in  this 
condition  will  not  give  the  spherical  distribution  of  the  light 
when  the  lamp  is  stationary.  A  standard  lamp  should  never 
be  spun. 

If  it  is  found  that  the  filament  under  measurement  bears  the 
process  of  spinning,  much  time  is  saved  in  studying  the  space 


*  Report  before  the  National  Electric  Light  Association ;   Electrical 
Engineer,  June  16,  1897,  page  676. 


216  PHOTOMETRIC  AL   MEASUREMENTS 

distribution  of  its  light,  as  only  readings  in  inclination  need  be 
made,  sparing  all  the  tedious  readings  in  azimuth ;  and  should 
the  conditions  be  entirely  favourable,  the  values  then  found 
will  more  correctly  integrate  the  mean  intensity  than  when  a 
mean  is  taken  of  the  usual  number  of  azimuth  readings. 

The  light  emitted  by  the  incandescent  lamp  being  so  constant, 
however  tedious  the  process  of  step  by  step  measurement,  the 
results  are  not  in  error  from  changes  in  the  light  strength  to 
be  measured. 

229.  The  calculation  of  the  measurements.  —  The  photometer 
bar  is  commonly  graduated  from  the  left,  and  it  is  customary 
to  place  the  standard  lamp  at  this  end.     The  measurements  are 
calculated  by  the  familiar  formula  applying  to  the  balanced 
setting  of  the  screen  at  a  distance  of  I  units  along  the  scale,  the 
total  distance  between  the  lights  compared  being  L  units.     The 
illuminating  power  of  the  lamp  photometered,  Iey  in  terms  of 
the  standard  lamp  /.,  is 

2  (88  bis) 

230.  The  measurement  of  the  spherical  intensity.*  —  For  con- 
venience the  tip  of  the  lamp  and  its  base  may  be  termed  the 
north  and  south  poles  respectively. 

The  lamp  is  placed  in  the  adjustable  holder  and  brought  into 
the  standard  position.  Thirteen  measurements  are  made  by 
rotating  the  lamp  horizontally,  each  interval  being  30°,  and  the 
last  measurement  checking  the  first. 

The  mean  of  the  thirteen  readings  will  give  the  mean  hori- 
zontal illuminating  power. 

Beginning  again  at  0°  azimuth,  thirteen  readings  are  made  in 
the  prime  meridian  or  vertical  circle,  the  interval  again  being 
30°,  and  the  last  reading  checking  the  first. 

*  Report  of  Franklin  Institute  Tests  on  Incandescent  Lamps,  page  11 ; 
and  Journal  of  the  Franklin  Institute,  September,  1885.  Also  consult 
Liebenthal,  Zeitschrift  fur  Instrumentenkunde,  19,  1899,  page  225. 


PHOTOMETRY  OF   THE  INCANDESCENT   LAMP        217 

It  will  be  noticed  that  four  readings,  two  being  check  read- 
ings, have  been  made  at  0°  azimuth.  The  mean  of  the  four  is 
taken  as  the  standard  reading,  it  being  the  value  of  the  intensity, 
should  the  lamp  be  used  as  a  standard. 

Additional  sets  of  thirteen  readings  each,  the  last  reading 
checking  the  first  one,  are  similarly  made  on  each  of  the  verti- 
cal circles  through  45°,  90°,  and  135°  azimuth. 

Sixty-five  measurements  in  all  are  thus  made,  and  in  com- 
bining them  for  the  mean  spherical  intensity,  a  note  is  taken 
of  the  repetitions,  such  as  four  measurements  each  at  the  north 
and  south  pole. 

Neglecting  the  repetitions,  which  may  also  be  omitted  in  part 
in  the  practice  of  the  method,  there  remain  thirty-eight  points 
on  the  reference  sphere,  whose  distribution  is :  — 

Distributed 
Values 

The  mean  of  four  measurements  at  the  north  pole  of  the  lamp       1 
Four  measurements  on  each  of  the  vertical  circles  through  0° 
and  90°  azimuth  at  vertical  circle  readings  of  60°,  120°,  240°,  and 

300° 8 

Four  measurements  on  each  of  the  vertical  circles  through  0°, 
45°,  90°,  and  135°  azimuth  at  vertical  circle  readings  of  30°,  150°, 

210°,  and  330° 16 

Twelve  measurements  30°  apart  at  the  equator  ...  12 
Four  null  values  at  the  south  pole  of  lamp  ....  1 
Total  number  of  effective  measurements  ....  38 

The  points  thus  laid  off  on  the  reference  sphere  are  approxi- 
mately equidistant,  being  somewhat  closer  together  at  the 
equator  than  at  the  poles. 

231.  When  the  lamp  is  rotated,  readings  are  taken  for  each 
15°  or  30°  in  inclination,  from  0°  to  90°,  and  from  0°  to  270°. 
These  are  integrated  values  for  their  corresponding  parallels  of 
latitude  on  the  unit  sphere. 

The  space  distribution  of  light  intensity  will  be  a  figure  of 
revolution.  A  curve  may  be  platted  from  these  readings,  from 
which  the  mean  spherical  intensity  may  be  obtained  (page  41) 


218  PHOTOMETKICAL   MEASUKEMENTS 

by  integrating  the  area  of  the  curve  with  a  planimeter,  and 
equating  the  area  to  the  mean  circle. 

232.  Observations   on   practical   and   laboratory   apparatus. — 

There  has  recently  been  a  marked  improvement  of  the  class  of 
photometers  termed  u  portable."  Formerly  such  an  apparatus 
possessed  questionable  value  as  a  measuring  instrument.  It 
was  operated  either  with  a  candle  or  an  oil  lamp  for  the  com- 
parison light;  and  these,  being  so  unreliable  under  the  best 
laboratory  conditions,  as  a  matter  of  course  proved  practically 
worthless  under  the  varied  conditions  of  promiscuous  testing. 
Since  the  perfection  of  the  incandescent  lamp  and  its  demon- 
strated reliability  as  a  working  standard  of  light,  the  portable 
photometer  has  been  improved  until  it  is  now  a  reasonably 
satisfactory  instrument. 

Such  an  apparatus  has  its  peculiar  requirements :  it  is  com- 
monly used  by  those  having  little  laboratory  experience,  and 
a  by  no  means  comprehensive  knowledge  of  the  principles 
involved  in  the  measurements  they  desire  to  accomplish. 
Their  demand  is  for  an  apparatus  reduced  to  the  simplest 
possible  elements  with  all  its  parts  so  adjusted  that,  by  follow- 
ing certain  plain  directions,  the  results  which  they  obtain  will 
have  a  reasonable  degree  of  certainty,  and  the  apparatus  shall 
prevent  them  from  making  the  errors  which  might  follow  from 
deficient  knowledge. 

Those  who  demand  "practical7'  apparatus  which  shall  do 
their  scientific  thinking  for  them,  are  only  too  prone  to  inveigh 
against  the  refinements  of  laboratory  apparatus  and  methods. 

233.  The   portable   photometer   for  incandescent   lamps. — A 

description  of  the  Queen  portable  photometer  will  be  given  as 
a  representative  of  the  advanced  design  of  such  apparatus. 
The  photometer  folds  compactly  and  is  carried  in  a  convenient 
case.  When  arranged  for  testing  (Fig.  56),  the  base  forms  a 
continuous  bench,  and  lateral  bellows  extend  from  the  sight 
box  to  the  compared  lights;  and  these  in  turn  are  covered 


PHOTOMETRY   OF   THE   INCANDESCENT   LAMP        219 


with  light-proof  hoods. 
The  standard  of  light  is 
a  calibrated  incandescent 
lamp.  The  sight  box 
is  of  the  conventional 
Bunsen  type  with  reflect- 
ing mirrors ;  and  the 
scale  is  marked  off  to  be 
direct  reading  in  candle 
units  (page  37).  The 
base  on  which  the  bench 
rests  is  in  reality  a 
switchboard  which  con- 
trols connections  similar 
to  those  shown  in  Fig. 
53,  with  the  exception 
that  a  rheostat  is  used 
in  each  lamp  circuit, 
permitting  independent 
control  of  the  voltage  at 
each  lamp.  Either  a 
voltmeter  and  ammeter, 
or  a  voltmeter  and  watt- 
meter, may  be  employed 
at  pleasure,  the  instru- 
ments being  switched 
successively  from  lamp 
to  lamp.  The  operation 
of  the  apparatus  should 
follow  the  precautions 
given  on  page  209.  By 
covering  the  sight  box 
with  a  light-proof  cloth 
the  photometer  may  be 
used  in  ordinary  light. 


CHAPTER   VII 

THE  ARC   LAMP   AND   ITS   PHOTOMETRY 

234.  The  subject  of  the  photometry  of  the  arc  lamp  is  beset 
with  especial  difficulties  and  uncertainties,  should  emphasis, 
by  such  an  expression,  be  placed  on  the  estimation  of  the  light 
of  the  arc  for  purposes  of  continuous  illumination,  rather  than 
on  the  specific  measurement  of  its  illuminating  power.  This 
distinction  is  insisted  upon  as  a  real  one,  for  the  measurement 
of  the  instantaneous  illuminating  power  of  the  arc  is  suscepti- 
ble of  practically  the  same  precision  as  the  measurement  of 
the  illuminating  power  of  the  incandescent  lamp. 

The  photometrical  expression  for  the  continuous  illuminating 
power  of  the  arc  light  has  an  applied  value  only  when  con- 
sidered in  connection  with  the  behaviour  and  properties  of  the 
arc  itself ;  otherwise,  such  expressions  are  misleading ;  and  the 
distinction  here  insisted  upon  has  been  so  generally  overlooked 
that  the  photometry  of  the  arc  light  has  come  to  be  regarded 
as  both  uncertain  and  valueless. 

Early  in  the  commercial  development  of  the  arc  light  cer- 
tain designations  were  introduced,  such  as  1200  and  2000  candle 
power,  based  on  the  supposed  maximum  candle  power,  which 
apparently  rated  the  illuminating  power  of  the  arc.  These  rat- 
ings were  soon  found  to  be  misleading,  and  since  the  illumi- 
nating power  was  considered  to  be  closely  proportional  to  the 
energy  transformed  in  the  arc,  a  rating,  such  as  450  watts  for  the 
2000  candle  power  lamp  was  proposed.  Present  practice  is  a 
modification  of  this  rating,  and  in  the  absence  of  a  generally 
accepted  basis,  lamps  are  commercially  adjusted  for  certain 
current  intensities,  and  the  potential  difference  at  which  the 

220 


THE  AKC   LAMP   AND   ITS   PHOTOMETRY  221 

arc  is  operated  is  governed  by  the  conditions  of  the  grouping 
of  lamps  in  the  circuit,  and  the  operation  of  the  lamps  with 
an  open  or  enclosed  arc. 

In  addition  to  a  previous  discussion  of  the  physics  of  the 
arc  (page  160)  there  are  other  details  upon  which  its  photo- 
metrical  practice  depends. 

235.  The  carbons.*  —  A  significant  distinction  amongst  car- 
bons is  their  degree  of  hardness,  which  may  range  from  the 
gray  metallic  appearance  of  graphitic  carbon,  to  the  dull  black 
colour  of  very  soft  and  friable  ones.     A  further  distinction 
arises  from  the  practice  of  coring  them,  which  is  applied  to 
carbons  of  extreme  or  medium  hardness,  the  core  consisting  of 
very  soft  carbon,  a  flux,  and  a  binding  material.     A  hard  carbon 
consumes  slowly,  and  burns  with  a  lower  efficiency,  or  requires 
more  watts  for  a  light  unit  than  a  softer  carbon. 

236.  The  quality  of  the  light.  —  This  is  to  a  certain  extent 
a  function  of  the  temperature  of   evaporation  of  the  carbon 
(see  page  163).     Hard  graphitic  carbon  has  a  higher  boiling 
point  than  that  which  has  a  soft  grain  and  is  dull  black  in  ap- 
pearance.   That  quality  of  light  which  may  be  termed  approxi- 
mately normal  white  light,  is  emitted  only  by  incandescent 
carbon  of  the  softest  variety  when  heated  to  its  boiling  point. 
The  hardness  of  the  carbon  seems  to  raise  its  boiling  point  and 
increases  the  intensity  of  the  higher  light  components,  so  that 
the  light  emitted  has  a  bluish  tinge. 

237.  The  emissivity  of  the  carbon  for  the  arc  light  follows 
the  same  relations  already  pointed  out  in  connection  with  the 
incandescent  filament  (page  172),  or,  in  general,  the  increased 
hardness  of  the  carbon  lowers  its  emissivity  for  light  radiations. 

*L.  B.  Marks,  Transactions  American  Institute  of  Electrical  Engi- 
neers, 7,  1890,  page  185;  and  W.  M.  S.,  Electrical  Engineer,  Oct.  3, 
1894,  and  Electrical  World,  Feb.  23,  1895,  page  223;  also  Blondel, 
L'Eclairage  Electrique,  March  13,  1897,  page  500. 


222  PHOTOMETRIC  AL   MEASUREMENTS 

238.  The  source  of  the  luminosity  of  the  arc.*  —  The  lumi- 
nosity is  principally  a  function  of  the  incandescent  state  of  the 
carbon.  It  is  experimentally  known  that  the  positive  carbon 
becomes  heated  to  the  temperature  of  ebullition,  and  the  vapour 
from  it  passes  to  the  negative  tip  of  the  arc.  The  positive  tip 
or  crater  of  the  carbon,  is  highly  incandescent,  while  the  nega- 
tive tip  is  only  feebly  so.  Thus  a  very  large  percentage  of  the 
total  illumination  of  the  arc  is  emitted  by  the  positive  crater, 
the  negative  tip  contributing  but  little,  while  the  arc  itself 
may  be  only  faintly  luminous,  or  brighter  according  to  certain 
conditions.  The  arc,  doubtless,  consists  principally  of  carbon 
vapour  and  to  some  extent  of  small  particles  of  finely  divided 
carbon  carried  over  mechanically ;  and  since  incandescent  gases 
are  only  feebly  luminous,  the  arc  can  contribute  but  little  to 
the  total  illumination  except  as  it  may  contain  particles  of  in- 
candescent matter.  Attempts  to  enrich  the  arc  by  introducing 
certain  hydrocarbons  f  into  it  have  not  succeeded  to  any  ex- 
tent, for  the  hydrocarbons  are  not  only  decomposed,  but  the 
high  temperature  of  the  arc  seems  to  vaporize  the  carbon, 
which  in  flames  of  lower  temperature  aggregates  into  small 
particles,  and  becoming  incandescent,  greatly  increase  the  lu- 
minosity of  the  flame.  The  difficulties  of  a  satisfactory  study 
of  the  arc  itself  have  so  far  proven  insuperable. 

When  the  arc  is  lengthened  to  any  considerable  extent,  the 
carbon  vapour  in  it  probably  becomes  superheated  and  intensi- 
fies the  violet  radiations  from  the  arc  as  a  whole. 

239.  The  carbon  points.  — After  the  carbon  has  been  operat- 
ing for  some  time  the  carbon  tips  attain  shapes  which  are  then 
maintained  fairly  uniform.  If  the  arc  is  an  open  and  continu- 
ous current  one,  the  positive  carbon  becomes  bluntly  pointed 
like  a  truncated  cone,  with  a  well-defined  crater  at  the  place 
where  the  arc  originates.  If  the  carbon  is  homogeneous  in  its 
grain  and  quality,  the  points  will  be  maintained  symmetrical 

*  W.  M.  S.,  Electrical  World,  April  6,  1895,  page  420. 

t  Journal  Institute  of  Electrical  Engineers,  1892,  page  375. 


THE   ARC   LAMP   AND   ITS   PHOTOMETRY  223 

to  the  axis  of  the  carbon,  though  the  edges  of  the  crater  will 
be  rounded  off.  But  should  such  a  carbon  be  cored  the  crater 
will  be  deeper,  with  regular  and  sharper  edges,  and  the  sym- 
metry of  the  cone  will  be  better  maintained.  With  carbons 
lacking  in  homogeneity  of  quality  and  structure,  a  soft  core  is 
a  great  aid  toward  their  symmetrical  consumption. 

The  negative  carbon  wears  to  a  more  decided  point  whose 
tapering  sides  are  somewhat  hollowed  out.  The  influence  of 
the  negative  carbon  on  the  luminosity  of  the  arc  is  so  slight 
that  there  is  no  necessity  for  using  an  especially  soft  or  a 
cored  carbon,  but  such  carbons  are  rather  to  be  avoided  since 
they  are  too  soft  under  the  impact  of  the  arc  stream,  and  wear- 
ing to  a  flat  cone  increase  the  unsteadiness  of  the  arc  and  de- 
crease the  total  illumination  by  a  greater  screening  action. 

When  the  arc  is  enclosed  within  the  usual  small  glass  cham- 
ber, the  pointing  of  the  carbons  is  greatly  modified.  The 
general  tendency  of  the  solid  carbons,  both  positive  and  nega- 
tive, is  to  wear  off  to  blunt  ends  with  slightly  rounded  edges. 
When  a  cored  positive  carbon  is  used  the  same  tendency  is 
seen,  except  in  this  case  the  centre  is  hollowed  out  by  a  more 
rapid  consumption  of  the  core.  The  tip  of  the  negative  carbon 
in  either  case  is  frequently  somewhat  irregular  in  outline,  and 
may  build  up  from  the  deposition  of  carbon  vapour  upon  it. 

240.  The  position  of  the  arc.  —  Under  normal  conditions  the 
arc  stream  passes  between  those  points  of  the  carbons  which 
are  least  distant ;  but  as  the  carbon  wears  away,  the  distance 
increases,  and  the  arc  is  transferred  to  adjacent  points,  and  in 
this  manner  travels  about  the  circumference  of  the  tips.  This 
action  seldom  proceeds  uniformly.  The  carbon  may  contain 
occluded  gases  which  cause  the  arc  to  flame  and  rapidly  change 
position.  Hard  particles  and  globules  of  foreign  matter,  such 
as  silica,  produce  rapid  shifting  of  the  arc.  These  and  other 
similar  causes  render  the  position  of  the  arc  inconstant.  The 
illuminating  power  in  any  direction,  and  the  total  illumination, 
too,  being  a  function  of  the  energy  transformed  within  it,  are 


224 


PHOTOMETRICAL  MEASUREMENTS 


constantly  changing  with  more  or  less  rapidity,  for  the  con- 
sumption of  the  carbons  lengthens  the  arc,  and  increases  its 
potential  difference,  which  further  assumes  a  different  value  as 
the  arc  changes  in  position.  As  the  distance  between  the  car- 
bons is  adjusted  by  the  regulation  of  the  lamp,  the  position  of 
the  arc  changes  and  its  illumination  is  modified.  These  dis- 
turbances exist  in  the  enclosed  arc  as  well,  but  the  changes  take 
place  much  more  slowly. 

241.  The  value  of  arc  light  photometry.  — It  is  these  changes 
which  cause  the  especial  difficulties  in  the  photometry  of  the 
arc  light  and  its  application  to  questions  of  illumination.  By 


310 


190 


/\ 


V 


V 


9  13 

FIG.  57. 


15 


18 


21  MINUTES 


the  adjustment  of  the  lamp  in  feeding  the  carbons,  the  total 
light  radiated,  and  its  space  distribution  as  well,  necessarily 
change,  and  may  even  fall  to  a  small  fraction  of  their  former 
values.  (See  Pig.  57.) 


THE    ARC   LAMP   AND   ITS   PHOTOMETRY  225 

The  distinction  emphasized  at  the  beginning  of  this  discus- 
sion may  now  be  enlarged  upon.  Except  in  cases  of  rapid 
adjustment  of  the  lamp  and  the  naming  of  the  carbons,  or 
mechanical  disturbances  of  the  arc,  its  illuminating  power  may 
be  measured  with  practically  as  great  exactness  as  that  of  the 
incandescent  lamp.  The  only  real  difficulty  which  the  pho- 
tometry of  the  arc  opposes  is  the  disparity  in  colour  of  light 
between  itself  and  that  of  any  secondary  standard  with  which 
it  may  be  compared.  But  it  must  be  noted  that  these  measure- 
ments yield  only  instantaneous  values  of  the  illuminating  power 
for  a  certain  radial  direction  from  the  arc.  The  fact  that  these 
instantaneous  values  are  not  maintained  is  the  one  which  ren- 
ders them  of  little  service  as  ratings  for  the  arc  lamp.  Not 
only  the  total  illumination  but  its  space  distribution  being 
inconstant,  a  photometrical  rating  of  the  arc  lamp  is  in  the  main 
meaningless. 

While  the  general  practice  of  arc  light  photometry  is  not 
advisable,  there  are  certain  cases,  other  than  those  of  pure 
research,  in  which  it  may  prove  valuable.  If  the  conditions 
are  carefully  selected,  and  the  measurements  are  made  by 
skilled  experimenters,  photometry  affords  reliable  information 
of  the  light-giving  qualities  of  carbons  and  the  absorption  of 
globes  and  envelopes,  and  of  the  efficiency  of  reflectors.  (Con- 
sult Appendix  A.) 

242.   The  properties   of   the    alternating   current   arc.  —  The 

polarity  of  certain  of  the  phenomena  of  the  electric  arc  having 
been  pointed  out,  the  alternating  current  arc  will,  for  purposes 
of  this  discussion,  be  considered  as  a  sequence  of  arcs  whose 
polarity  is  periodically  reversed,  and  that  each  one  in  the  series 
possesses  all  the  properties  of  the  constant  polarity  arc.*  The 
pointing  of  the  carbons  is  modified,  and  each  tip  in  succession 
being  the  positive  one,  forms  the  characteristic  crater.  Either 

*  W.  L.  Puffer,  Transactions  American  Institute  of  Electrical  Engi- 
neers, 13,  1896,  page  71. 
Q 


226  PHOTOMETRICAL   MEASUREMENTS 

one  or  both  carbons  may  be  cored,  and  the  arc  may  be  open  or 
enclosed. 

243.  The  space  distribution  of  the  intensity  of  illumination.  — 

This  has  already  been  shown  to  vary  with  each  change  in  the 
position  of  the  arc,  and  the  conformation  of  the  crater,  and  the 
variation  in  quality  of  the  carbon  consumed.  Were  the  arc 
perfectly  constant  in  position  and  properties,  the  space  distri- 
bution of  its  illumination  would  become  an  important  function, 
and  could  be  determined  with  great  accuracy.  The  practical 
importance  attaching  to  this  quantity,  is,  however,  a  question 
rather  of  illumination  than  of  photometry.  For  the  latter  the 
instantaneous  intensities  (especially  the  horizontal  and  the 
maximum)  are  the  elements  of  importance,  the  mean  spherical 
intensity  having  only  a  scientific  value.  While  each  measure- 
ment in  a  series  from  which  the  space  distribution  is  calculated 
may  be  accurate  in  itself,  the  inconstant  behaviour  of  the  arc 
renders  the  mean  obtained  only  an  approximate,  working  one. 

244.  The  continuous  current  arc  exhibits  a  space  distribution 
of  illumination  which  is  typically  illustrated  in  Figure  58,  in 
which  the  illuminating  power  of  an  arc  supposed  to  be  located 
at  0  has  been  platted  by  polar  coordinates.      The  maximum 
illuminating  power  is  seen  to  occur  at  40°  inclination.      The 
inclination  and  value  of  the  maximum  radius  vector  varies  from 
time  to  time  in  any  given  arc,  and  between  different  arcs  as 
well ;  *  usually  the  inclination  of  the  maximum  radius  vector 
lies  between  40  and  50  degrees.      The  outline  of  such  polar 
curves  is  roughly  elliptical,  and  a  number  of  investigators  have 
deduced  from  its  geometrical  properties  certain  functions  which 
enable  approximate  values  of  the  illuminating  power  to  be 
calculated  for  any  desired  inclination,  f      The  horizontal  illu- 

*  Consult  Report  of  Franklin  Institute  Tests,  V,  1885. 

t  Trotter,  Journal  Institute  of  Electrical  Engineers,  1892,  page  360 ; 
and  Voit,  Bericht  der  International  Elektrisch  Ausstellung  zu  Miinchen, 
1882,  pages  104  and  139 ;  also  Gerard,  Centralblatt  fur  Electrotechnik, 
January,  1890 ;  and  Palaz,  La  Lumiere  Electrique,  37,  1890,  page  415. 


THE   ABC   LAMP   AND   ITS   PHOTOMETRY 


227 


minating   intensity,  which  is  most  readily  photometered,  is 
about  20  per  cent  of  the  maximum  value. 

The  contributions  of  the  three  elements  producing  the  total 
illumination — the  positive  and  negative  carbon  tips  and  the 
arc  —  may  be  approximately  ascertained  from  such  curves. 


TO  60 

FIG.  58. 

The  interior  of  the  positive  crater  is  the  principal  source  of 
light,  and  the  small  relative  horizontal  increment  is  due  both  to 
the  arc  stream  and  the  negative  tip.  The  positive  carbon  being 
the  prime  light  source,  the  maximum  intensity  should  occur  in 
a  radius  normal  to  its  plane,  which  if  the  crater  is  symmetrically 
located  would  be  in  the  axis  of  the  carbon.  The  illuminating 
power  at  any  other  point  would  vary  from  this  as  the  cosine  of 
its  inclination  (Lambert's  law),  according  to  Trotter.*  That 

*  Reference  cited. 


228 


PHOTOMETRICAL  MEASUREMENTS 


the  maximum  intensity  occurs  not  at  90°  but  at  45°  to  the  hori- 
zontal, is  due  to  the  screening  action  of  the  negative  tip.     This 

seems  well  borne  out 
by  the  polar  curves  of 
the  arc.  In  Figure  59 
Trotter  has  platted  the 
polar  curve  of  cosines 
with  the  polar  curve 
of  the  arc. 

Polar  curves  of  the 
arc  are  also  valuable  for 
studying  the  influence 
which  the  quality  of 
the  carbon,  their  shape 
and  adjustment,  has  on 
the  space  distribution 
of  the  illumination. 

The  alternating  cur- 
rent arc  being  a  series 
of  periodically  re- 
versed continuous  cur- 
rent arcs,  their  virtual 
space  distribution  of 
illuminating  power  is 
closely  given  by  dupli- 
cating the  polar  curve 
just  described  above 
the  horizontal  radius 
vector,  as  shown  in 
FIG.  59.  Figure  60.  At  each 

alternation  the  posi- 
tive tip  becoming  the  negative  tip  for  the  following  half 
period,  cools  down  from  the  state  of  high  incandescence  of 
the  positive  crater,  without  in  any  case  reaching  the  low  tem- 
perature which  it  would  attain  with  a  continuous  current,  and 
this  heightened  incandescence  of  the  negative  tip  very  inateri- 


THE   ABC    LAMP    AND   ITS   PHOTOMETRY 


229 


ally  increases  the  horizontal  intensity.  This  distinction  is 
very  strongly  emphasized  in  the  enclosed  arc.  (Compare  Fig- 
ures 58  and  61). 

245.  The  enclosed  arc,*  whether  supplied  by  a  continuous  or 
alternating  current,  shows  a  space  distribution  of  illuminating 
power  which  is  much  affected  by  its  enclosure. 


In  the  main  the  effect  of  an  envelope  tends  toward  a  more 
uniform  distribution  of  light.  Both  the  character  and  the  con- 
dition of  the  envelope  have  a  modifying  influence.  If  the  glass 

*  L.  B.  Marks,  Proceedings  International  Electrical  Congress,  1893, 
page  387.  L.  B.  Marks,  Electrical  World,  Jan.  30,  1897,  page  174  ;  also 
Freedman,  Transactions  American  Institute  of  Electrical  Engineers,  14, 
1897,  page  425  ;  and  Matthews,  Transactions  American  Institute  of  Elec- 
trical Engineers,  15,  1898,  page  579. 


230 


PHOTOMETRIC AL  MEASUREMENTS 


has  a  inatt  surface,  the  total  illumination  is  reduced  and  a 
fairly  uniform  space  distribution  results.  Even  with  the  purest 
carbons  a  gray  coating  forms  on  the  interior  of  the  chamber, 


400  C-ANDLES  500 


40° 


and  this  has  much  the  same  effect  as  the  frosting  of  the  glass, 
excepting  that  it  changes  the  quality  of  the  light  transmitted, 
by  selective  absorption  of  the  violet  rays. 

When  the  arc  is  open  to  the  air,  changes  take  place  within 
it  very  rapidly,  while  enclosing  it  in  an  envelope  greatly  tends 
to  steady  it.  The  carbons  wear  away  very  slowly,  and  there  is 
freedom  from  sudden  cooling,  with  the  result  of  a  marked  con- 
stancy in  the  distribution  of  light.  The  photometry  of  such 
arcs  is  not  only  more  easily  and  rapidly  performed,  but  the 
polar  curves  from  such  measurements  have  a  greater  practical 
value  than  in  the  case  of  the  open  arc.  While  the  photometry 
of  the  open  arc  is  not  to  be  encouraged  in  general  practice, 
except  for  purposes  already  pointed  out,  that  of  the  enclosed 
arc  bids  fair  to  assume  considerable  practical  importance. 


THE   AKC    LAMP   AND   ITS   PHOTOMETRY  231 

246.   The  mean  spherical  intensity  of  illumination  of  the  arc 

has  already  been  alluded  to  as  a  quantity  having  rather  scien- 
tific than  practical  interest.  The  intensity  of  the  illumination 
in  a  definite  direction  is  the  only  fact  of  value  when  considering 
the  illumination  from  the  arc  light,  the  mean  or  average  value 
for  all  directions  is  of  no  consequence.  It  is  a  useful  device, 
however,  when  a  comparison  is  made  between  several  arcs  or 
the  same  arc  under  varied  conditions,  involving  a  study  of  the 
total  luminous  radiation.  Of  its  practical  significance,  Trotter5* 
has  said  that  "  with  a  scientific  but  misguided  regard  for  the 
truth,  the  candle  power  of  arc  lamps  has  been  reduced  to  its 
mean  spherical  value  by  many  authorities." 

The  quantity  may  be  estimated  from  the  intensity  curves, 
(page  41),  integrating  them  either  mechanically  or  graphically, 
or  by  traversing  the  arc  spherically.  If  the  intensity  curve  is 
platted  from  the  mean  of  a  number  of  readings  taken  at  suf- 
ficient time  intervals  to  represent  the  average  behaviour  of  the 
lamp,  it  may  be  assumed  that  these  values  will  define  the  mean 
spherical  distribution  of  the  light,  and  that  the  spherical 
intensity  distribution  is  a  figure  of  revolution  symmetrical 
about  the  axis  of  the  carbons,  and  generated  by  the  intensity 
curve. 

Attempts  have  been  made  to  obtain  a  function  connecting  the 
readily  measurable  horizontal  and  maximum  intensities  with 
the  mean  spherical  candle  power.  It  has  already  been  shown 
that  such  a  function  can  not  exist  in  the  nature  of  the  case. 
Gerard  f  mentions  an  empirical  one  which  was  formerly  largely 
used  :  that  the  mean  hemispherical  candle  power,  S,  is  related 
to  the  horizontal  candle  power,  H,  and  the  maximum  candle 
power,  M)  by  the  expression,  — 

S  =      +M.  (97) 


*  Journal  Institute  of  Electrical  Engineers,  1892,  page  375. 
t  M.  Gerard,  "Candle  Power  of  Arc  Lamps,"  Centralblatt  fiir  Elektro- 
technik,  January,  1890. 


232  PHOTOMETRICAL  MEASUREMENTS 

247.  The  efficiency  of  the  arc  lamp  *  may  be  variously  stated 
according  to  the  meaning  placed  on  the  term.     As  a  purely 
physical  statement  the  radiant  efficiency  of  the  arc  is  the  ratio 
between  the  luminous  energy  radiated  and  the  total  energy 
transformed  in  the  arc ;  a  quantity  which  has  also  been  called 
the  optical  efficiency.    The  mean  hemispherical  efficiency  of  the 
enclosed  arc  with  the  continuous  current  is  stated  by  Marks  f 
to  be  8.4  per  cent ;  while  that  of  the  open  arc  is  about  10  per 
cent. 

THE  PRACTICE   OF  ARC  LIGHT  PHOTOMETRY 

248.  The  comparison  light.  —  In  the  previous  discussion  of 
standard  and  reference  lights,  the  constancy  of  the  light  and 
the  accuracy  of  reproduction  were  the  primary  considerations, 
though  attention  was  called  to  the  quality  of  the  illumination ; 
but  in  the  photometry  of  the  arc  light  the  colour  of  the  light 
is  of  the  first  importance. 

Though  such  devices  as  the  Lummer-Brodhun  contrast 
optical  screen  and  the  flicker  photometer  yield  good  results 
in  special  cases,  the  general  photometrical  comparison  of  lights 
which  differ  to  any  extent  in  colour,  has  been  seen  to  be  difficult 
and  more  or  less  uncertain.  Spectrophotometry  affords  an  ac- 
curate means  for  comparing  the  intensities  of  definite  colour 
constituents  of  the  light,  but  such  data  give  little  information 
concerning  the  illuminating  properties  of  the  light.  There 
remains  the  criterion  for  the  accurate  photometry  of  arc  lights 
that  comparisons  be  made  only  between  equally  lighted  and 
similarly  coloured  fields. 

The  incandescent  lamp  is  the  one  standard  whose  quality  of 
light  may  be  made  to  approach  closely  to  that  of  the  arc.  The 

*  "  The  Efficiency  of  the  Arc  Lamp,"  H.  Nakano,  Transactions  American 
Institute  of  Electrical  Engineers,  6,  1889,  page  308.  Also,  "  The  Efficiency 
of  Light  Sources,"  E.  L.  Nichols,  Transactions  American  Institute  of  Elec- 
trical Engineers,  8,  1891,  page  214. 

t  Proceedings  International  Electrical  Congress,  1893,  page  390. 


THE  ABC   LAMP   AND   ITS   PHOTOMETRY  233 

quality  of  the  arc  light  may  vary  from  slightly  yellowish 
white,  through  clear  white  to  a  bluish  white,  which  idiosyn- 
crasies of  tint  may  be  closely  imitated  by  varying  the  voltage 
applied  to  the  incandescent  lamp.  But  these  considerations 
finally  resolve  themselves  into  a  comparison  with  the  adopted 
primary  light  standard  in  order  that  the  arc  may  be  evaluated 
in  terms  of  the  primary  unit.  This  is  the  most  pronounced  of 
the  many  difficulties  incident  to  the  photometry  of  the  arc 
light.  In  the  present  stage  of  the  development  of  arc  light 
photometry,  this  light  must  be  ultimately  compared  with  the 
amyl  acetate  flame,  or  the  illuminating  power  of  a  bluish  white 
light  must  be  expressed  in  terms  of  a  distinctly  reddish  flame. 
The  question,  being  ultimately  a  physiological  one,  no  function 
is  known,  —  and  from  the  results  of  repeated  experimental 
attempts  it  appears  to  be  impossible  of  attainment,  —  which 
shall  exactly  connect  the  illuminating  powers  of  differently 
coloured  lights.  The  adoption  of  an  especial  standard  of  illu- 
minating power  for  arc  lights  whose  quality  of  light  shall  be 
the  same  as  that  of  the  arc  itself  has  been  advocated,  but 
against  this  is  urged  the  valid  objection  of  the  undue  multi- 
plication of  standards  and  units. 

249.  The  incandescent  lamp  standard.  —  The  only  plan  avail- 
able to  the  photometrician  is  to  arrive  at  a  working  incandes- 
cent lamp  standard,  by  a  series  of  differentiations,  beginning 
with  the  amyl  acetate  flame  and  varying  the  colour  of  the  com- 
pared light  slightly  in  each  case.  This  result  is  unsatisfactory 
and  can  not  lead  to  accurate  statement.  Apparently  no  light 
is  sufficiently  defined  when  it  is  stated  to  yield  certain  units  of 
illuminating  power,  without  at  the  same  time  specifying  the 
quality  of  the  light.  If  illumination  is  taken  to  mean  the 
extent  to  which  it  enables  objects  to  be  clearly  defined,  then 
in  this  limited  sense  the  illuminating  power  of  the  arc  light 
may  be  expressed  in  amyl  acetate  units. 

Two  methods  are  open  to  the  photometrician:  to  secure  a 
reliably  calibrated  incandescent  lamp  from  some  authoritative 


234  PHOTOMETBICAL  MEASUREMENTS 

laboratory ;  *  or  to  accomplish  the  calibration  of  the  incandes- 
cent lamp  directly  from  the  primary  standard. 

250.  The  calibration  of  the  incandescent  lamp.  —  For  this  pur- 
pose the  flicker  photometer  or  the  Lummer-Brodhun  optical 
screen  are  to  be  preferred,  though  a  skilled  photometrician 
may  perform  the  calibration  satisfactorily  with  a  Bun  sen 
screen.  In  any  case,  the  first  comparison  will  be  between 
the  amyl  acetate  flame  and  the  selected  incandescent  lamp. 
This  should  be  brought  to  yield  a  light  slightly  whiter  than 
the  amyl  acetate  flame.  After  a  satisfactory  value  for  this 
incandescent  lamp  has  been  found,  a  second  incandescent  lamp 
is  in  turn  compared  with  it,  the  voltage  of  the  first  lamp  being 
maintained  at  the  same  value  used  in  the  first  comparison; 
while  the  second  lamp  is  burned  yet  brighter  than  the  first  one. 
By  repeating  this  process  between  the  same  or  different  lamps 
arid  increasing  the  intensity  of  incandescence  at  each  compari- 
son, the  desired  tint  is  at  length  reached  and  the  intensity  of 
illumination  is  in  a  measure  expressed  by  this  step-up  process 
in  terms  of  the  amyl  acetate  standard. 

When  the  incandescence  of  a  lamp  is  raised  to  such  a  degree 
that  the  light  emitted  is  bluish  white,  the  temperature  is  so 
high  that  the  carbon  is  near  the  plastic  state,  and  slowly 
volatilizes,  and  the  lamp  will  not  continue  to  emit  a  constant 
illuminating  power  for  any  length  of  time.  Before  using  a 
calibrated  lamp  in  practice,  it  is  well  to  standardize  several 
lamps  against  it,  and  reserve  these  to  check  the  working 
standard  from  time  to  time. 

A  calibration  curve  may  be  obtained  for  the  working  lamp 
between  its  illuminating  power  and  the  voltage  (page  183) 
which  will  be  of  assistance  when  it  becomes  necessary  to  adjust 
its  incandescence  to  accord  with  the  different  tint  of  the  arc 
light.  Attention  is  again  called  to  the  necessity  for  using  a 

*  Consult  the  Electrical  World  and  Engineer,  editorial,  July  8,  1899, 
page  39 ;  also  Doane,  Transactions  American  Institute  of  Electrical 
Engineers,  1899. 


THE   ARC   LAMP   AND   ITS   PHOTOMETRY  235 

sensitive  and  accurately  calibrated  voltmeter  with  the  standard 
incandescent  lamp  and  for  supplying  it  with  a  current  from  a 
storage  battery. 

The  size  of  the  incandescent  lamp  to  employ  as  a  working 
standard  depends  on  the  dimensions  of  the  photometrical  train ; 
in  order  to  shorten  the  distance  between  the  screen  and  the 
arc  light  it  may  be  necessary  to  use  a  high  power  lamp.  In 
any  case  very  strong  illumination  of  the  screen  is  to  be  avoided, 
as  it  renders  the  eye  less  sensitive.  The  fact,  too,  that  the 
lamp  is  burned  in  excess  of  its  normal  rating  must  be  taken 
into  account  when  selecting  a  lamp  for  a  certain  working  power 
of  the  standard. 

251.  Mirrors  are  a  useful  adjunct  to  a  photometer  train. 
They  require  to  be  kept  scrupulously  clean  and  should  have 
the  surface  free  from  scratches.  They  need  to  be  calibrated  for 
position,  for  a  certain  portion  of  the  incident  light  is  absorbed, 
and  some  light  is  irregularly  reflected.  The  quality  of  the 
light  is  also  affected  by  selective  absorption,  a  property  of 
the  mirror  which  varies  in  intensity  with  the  inclination  of 
the  incident  light;  while  some  experimenters  have  failed  to 
find  the  action  appreciable.* 

If  the  mirror  is  to  be  used  in  an  angular  position  which  will 
require  continued  adjustment  to  the  position  of  the  radiant, 
it  should  be  provided  with  an  index  quadrant,  and  be  cali- 
brated for  changes  of  the  angular  position.  Frequently  mir- 
rors are  used  at  a  fixed  angle  of  about  45°;  and  the  loss  of 
light  can  be  determined  for  this  set  position. 

Incandescent  lamps  are  preferable  for  such  calibration  work 
and  this  may  be  performed  on  the  usual  photometer  bench. 
The  lamps  are  first  compared  directly,  one  being  mounted  on 
some  radial  device,  which  will  enable  a  fixed  distance  between 
the  lamps  to  be  maintained  when  the  mirror  is  introduced  at 

*  Matthews,  Transactions  American  Institute  of  Electrical  Engineers, 
15, 1898,  page  583. 


236  PHOTOMETRICAL  MEASUREMENTS 

any  reflecting  angle.*      Then  comparisons  are  made  with  the 
mirror  set  at  the  desired  angle. 

If  the  illuminating  power  of  one  lamp  in  terms  of  the  other, 
without  the  use  of  the  mirror,  is  b»  and  with  the  mirror  is  62, 
the  coefficient  of  diminution  of  the  light  c  will  have  a  value 

c=4*.  (98) 

&i 

A  convenient  correction  factor  a  is  obtained  by  making 

a  =  i  =  £-  (99) 

c     02 

When  the  mirror  is  used  with  an  arc  lamp,  the  illuminating 
power  of  the  arc  after  reflection,  72  is  too  small,  owing  to  loss 
of  light  by  the  mirror;  its  value  7j,  which  would  have  been 
obtained  had  its  light  passed  directly  to  the  screen  is  then 

/!  =  a/2,  (100) 

which  is  the  working  equation  for  such  corrections. 

An  elaborately  mounted  mirror  is  not  a  necessity;  one  may 
be  improvised  with  a  piece  of  heavy  plate  glass,  at  most  six 
inches  square,  whose  surface  is  truly  plane.  If  the  mirror  is 
to  be  used  in  a  fixed  position  after  adjustment  to  the  desired 
reflecting  angle,  a  socket  joint  is  the  best  attachment  for  the 
mounting.  Should  it  be  desired  to  make  successive  angular 
adjustments,  the  mirror  should  be  movable  about  a  horizontal 
axis,  which  should  lie  in  the  optical  axis  of  the  photometer 
bench. 

252.  The  suspension  of  the  arc  lamp  for  the  measurement  of 
the  illuminating  power  will  depend  upon  the  photometrical 
method  to  be  followed.  If  merely  the  horizontal  intensity  is 
to  be  photometered  for  various  points  in  azimuth,  the  lamp  will 
require  only  a  simple  suspension  to  bring  the  arc  itself  into 

*  Matthews,  ref.  cit.,  page  581. 


THE   ARC   LAMP   AND   ITS   PHOTOMETRY  237 

the  photometrical  axis,  with  some  device  for  turning  it 
in  azimuth  and  indicating  its  angular  position.  Obviously 
the  photometer  can  not  be  made  to  traverse  the  arc  spheri- 
cally, but  this  is  indirectly  accomplished  by  using  reflecting 
mirrors, 

By  one  method,  which  has  been  frequently  used,*  the  arc 
is  traversed  by  a  mirror  attached  to  a  short  arm,  movable 
about  an  axis  bolted  to  the  frame  of  the  arc  lamp.  This  is  a 
tedious  method,  and  necessitates  numerous  adjustments  of  the 
mirror. 

A  preferable  method  is  to  swing  the  arc  lamp  from  an  upper 
vertex  of  a  jointed  rectangular  frame,  the  opposite  side  of  which 
is  rigidly  fastened  in  the  vertical  plane  through  the  photo- 
metrical  axis,  the  mirror  being  mounted  at  the  diagonal  vertex, 
and  with  its  centre  in  the  photometrical  axis  and  moved  by 
the  lower  member  of  the  frame,  the  lamp  being  so  suspended 
that  the  arc  lies  in  the  axis  of  the  member  and  at  a  distance  of 
about  four  feet  from  the  mirror.  An  index  finger  may  be 
attached  to  the  frame  for  indicating  its  inclination.  The  arc 
must  move  in  a  plane  perpendicular  to  the  photometrical  axis, 
and  preferably  in  the  same  plane  which  contains  the  centre  of 
the  mirror,  an  adjustment  readily  effected  when  the  frame  is 
horizontal. 

Various  other  suspensions  will  doubtless  suggest  themselves, 
yet  it  is  advisable  to  adopt  a  method  which  will  maintain  a 
fixed  distance  between  the  arc  and  mirror. 

253.  The  arrangement  of  the  photometer  train. — The  photom- 
eter train  will  include  the  bench  and  its  accessories,  the 
mirror,  the  suspension  frame  and  the  arc,  together  with  any 
light -diminishing  devices.  Since  all  arrangements  involve 
essentially  similar  photometrical  principles,  a  typical  case  is 

*  Franklin  Institute  Tests,  ref .  cit. ;  also  Journal  Institute  of  Electrical 
Engineers,  1892,  page  360 ;  Elektrotech.  Zeitschrif t,  1883,  page  444,  and 
1887,  page  357. 


238 


PHOTOMETRICAL   MEASUREMENTS 


illustrative :  this  is  shown  in  outline  in  Figure  62.  The  photo* 
meter  bench  AB  may  have  a  working  length  of  either  100  inches, 
2  metres,  or  even  less  with  a  light-reducing  device.  Both  the 
standard  light  S  and  the  photometer  screen  G  are  operated  in 
the  usual  positions. 

The  photometer  bench  may  be  placed  in  a  separate  room,  or 
enclosed  in  a  light-proof  canopy.  The  light  from  the  arc  is 
admitted  through  a  boxed  opening  approximately  the  size  of 
the  optical  screen,  and  placed  directly  in  the  photometrical 
axis,  the  opening  being  through  a  chamber  whose  sides  are  suffi- 
ciently separated  to  prevent  the  admission  of  extraneous  light. 


FIG.  62. 

A  revolving  sector-disk  is  placed  at  Z>,  just  beyond  the  opening 
The  reflecting  mirror  is  at  Jf,  and  the  arc  to  be  photometered  is 
located  at  L. 

The  distance  between  L  and  S,  measured  with  reference  to 
the  centre  of  the  mirror,  is  taken  at  5  metres,  or,  if  the 
dimensions  are  in  English  measure,  for  ready  calculation  it 
may  be  made  20  feet.  It  is  to  be  understood  that  these 
dimensions  are  merely  suggestive,  and  in  some  cases  they  may 
be  exceeded  to  an  advantage,  though  a  shorter  length  than  5 
metres  is  not  advisable. 


THE   ARC   LAMP   AND   ITS   PHOTOMETRY  239 

A  rotating  sector-disk  will  prove  a  useful  adjunct  to  the 
photometer  train,  though  it  is  not  a  necessity,  provided  the 
distance  between  the  standard  light  and  the  arc  can  be  made 
sufficiently  large.  The  diameter  of  the  disk  may  be  8  or 
10  inches;  the  relative  area  of  the  openings,  the  speed  at 
which  it  should  be  operated,  and  the  coefficient  of  its  diminu- 
tion of  the  light  have  already  been  discussed  (page  24). 

254.  The  photometer  adjustments.  — The  maximum  sensitive- 
ness of  the  adjustment  of  the  screen  occurs  for  a  given  interval 
between  the  lights,  when  a  balance  is  obtained  midway  of  the 
illuminations  compared;  and  while  the  general  tendency  in 
photometrical  measurements  should  be  toward  this  condition, 
yet,  on  account  of  the  great  inequalities  in  the  lights  compared, 
the  condition  operates  only  as  a  tendency.    It  may  be  approached, 
however,  by  employing  high  illuminating  power  in  the  stand- 
ard light,  or  diminishing  the  light  of  the  arc,  and  especially  by 
a  combination  of  these  expedients.     The  sensitiveness  in  the 
setting  of  the  screen  is  also  increased  by  lengthening  the  dis- 
tance between  the  compared  lights. 

Specific  directions  can  not  be  given  governing  the  illuminat- 
ing power  of  the  standard  light  and  the  various  dimensional 
details  of  the  photometrical  train;  these  must  be  determined 
for  individual  cases,  and  can  readily  be  decided  upon  after 
making  preliminary  calculations. 

The  brilliant  illumination  of  any  photometrical  screen  is 
to  be  avoided,  for  in  weak  light  the  eye  is  more  sensitive 
to  changes  in  the  illumination.  Similarly,  the  employment  of 
a  sectored  disk  is  advisable  for  reducing  the  intensity  of  the 
arc  light;  the  fatigue  of  the  eye  is  less  in  weaker  light. 

255.  In  illustration  of  some  of  these  details,  the  distance 
between  the  arc  and  the   standard  lights  will  be  taken  at 
500   centimetres.     Suppose  the  screen  is  at  a  distance  of   I 
centimetres  from  the  standard,  then  to  decrease  the  light  falling 
upon  it  by  one-hundredth  part,  the  distance  between  the  two 


240  PHOTOMETRICAL   MEASUREMENTS 

must  be  increased  x  centimetres,  and  applying  the  photomet- 
rical  law  of  inverse  squares, 


(101) 

Two  initial  positions  of  the  screen  may  be  taken,  giving  I 
the  values  of  15  and  90  centimetres,  and  the  corresponding 
values  of  x  are  found  to  be  0.075  and  0.45  centimetres.  These 
values  express,  in  a  manner,  the  relative  sensitiveness  of  the 
adjustment  of  the  screen.  The  range  of  movement,  when  the 
screen  is  at  a  distance  of  90  centimetres,  for  a  visible  change  of 
the  light  falling  on  the  screen,  is  so  much  greater  than  in  the 
former  case  that  it  leads  both  to  greater  ease  of  work  and 
exactness,  for  a  slight  error  in  the  estimation  of  the  distance  I 
will  be  of  less  consequence,  the  greater  it  is  made. 

For  the  sake  of  simplicity,  the  light  falling  on  the  screen 
from  one  source  only  has  been  considered.  In  a  rigid  in- 
vestigation of  the  adjustment  the  contrast  difference  of  the 
one-hundredth  part  would  be  taken  between  the  light  on  the 
screen  from  each  source,  which  would  lead  to  complicated 
mathematical  expressions.  At  a  screen  distance  of  only  15 
centimetres  the  above  analysis  is  not  appreciably  in  error. 

Denoting  the  illuminating  power  of  the  arc  by  J0,  and  of  the 
standard  by  /„  for  a  distance  between  these  of  500  centimetres, 

(102) 


If  7,  be  one  light  unit,  and  I  15  centimetres, 
ra  =  1045  light  units, 

and  if  It  has  an  intensity  of  50  light  units,  and  I  be  90  centi- 

metres, then 

I"a  =  1038  light  units. 

This  clearly  shows  that,  for  the  photometry  of  a  given  lumi- 
nous intensity  of  the  arc  light,  a  high-power  comparison  light, 


THE   ARC   LAMP   AND   ITS   PHOTOMETRY  241 

when  no  light-reducing  device  is  used,  leads  to  increased  sen- 
sitiveness in  the  setting  of  the  screen,  and  diminishes  the 
influence  of  the  errors  of  adjustment  and  measurement. 

256.  Sundry  details. — In  addition  to  the  general  directions 
for  the  preparation  of  the  photometer  room  (page  198),  if  the 
arc  lamp  be  suspended  in  an  outer  room,  its  walls  must  be  as 
carefully  blackened  as  those  of  the  room  in  which  the  photom- 
eter bench  is  placed.     All  portions  of  the  photometer  train 
must  be  given  a  dull  black  finish,  and  if  the  arc  lamp  has 
bright  metallic  parts,  these  must  be  covered  with  some  non- 
reflecting  material. 

Two  operators  will  be  necessary  for  such  tests,  one  to 
adjust  the  position  of  the  arc,  and  a  second  to  make  the 
adjustment  of  the  screen.  The  latter  operator  should  avoid 
looking  at  the  arc  light  or  the  reflecting  mirror,  and  not 
attempt  an  adjustment  of  the  screen  until  the  eyes  have 
become  rested  from  the  external  light. 

257.  The  calculations  of  the  illuminating  power  are  made  after 
the  general  photometrical  equation  on  page  207. 

Denoting  the  distance  between  the  lights  by  L,  and  between 
the  screen  and  the  light  standard  by  /,  the  illuminating  power 
of  the  arc  by  /a,  and  the  standard  by  /„  then,  as  before,  from 
equation  88, 

(103) 

provided  no  light-reducing  device  has  been  used  between  the 
arc  and  the  screen.  If  a  rotating  sector-disk  has  been  em- 
ployed, whose  correction  factor  is  a,  then  the  previous  equa- 
tion reads, 

(104) 

258.  The  measurement  of    the   intensity   of    powerful   light 
sources.  — The  facilities  of  the  ordinary  photometer  room  are  not 


242 


PHOTOMETRICAL  MEASUREMENTS 


adapted  for  measuring  the  illuminating  power  of  light  sources, 
whose  intensity  greatly  exceeds  that  of  arc  lights  in  common 
use.  This  is  especially  the  case  with  search  lights. 

The  optical  bench  available  in  the  photometer  room,  if  it  is 
equipped  with  a  Lummer-Brodhun  optical  screen,  may  be 
adapted  for  this  work  by  interposing  one  or  more  opal  glass 
diffusing  and  absorbing  screens  between  the  sight  box  and  the 
light  source.  The  details  for  such  practice  will  be  found 
clearly  outlined  in  the  discussion  of  the  Weber  photometer 
(pages  82-85).  This  apparatus,  however,  is  preferable  for 
such  work,  on  account  of  its  flexibility  and  portability. 


APPENDIX 

A.  THE  ABSORPTION  OF  LIGHT  BY  GLOBES  AND 

THE  ACTION  OF  REFLECTORS. 

B.  RECENT  INVESTIGATIONS  OF  LAMBERT'S  LAW 

FOR  THE  REFLECTION  OF  LIGHT. 

C.  TABLE    OF    RATIOS    FOB...  A    100-PART    PHO- 

TOMETER BAR. 


OF  THE 

UNJVEHSJTY 


A.      THE    ABSORPTION     OF    LIGHT     BY    GLOBES    AND 
THE    ACTION    OP    REFLECTORS 

THOUGH  the  technical  importance  of  this  subject  is  immedi- 
ately apparent,  it  has  received  little  precise  investigation.  The 
great  variety  of  globes  and  reflectors  in  use,  and  the  prevailing 
conditions  under  which  they  are  employed,  are  scarcely  amen- 
able to  classification  and  precise  treatment.  These  matters  are 
details  for  a  thorough  science  of  illumination,  if  it  is  a  possi- 
bility of  the  future  that  such  a  science  will  be  developed. 

Several  investigations  of  the  absorption  of  light  by  globes 
have  been  published ;  *  and  one  of  the  most  practical  of  these 
studies  has  recently  been  accomplished  by  Williamson  and 
Klinck,  who  have  experimented  on  the  globes  and  reflectors  in 
common  use  with  gas  and  electric  lights. t  The  present  dis- 
cussion is  largely  abstracted  from  their  paper  before  the 
Franklin  Institute. 

Globes  and  reflectors  modify  the  intensity,  light  quality,  and 
intrinsic  brightness  of  a  light  source  in  several  ways :  (a)  the 
radiations  falling  on  the  surface  of  the  globe  or  reflector  suffer 
partial  absorption,  and  are  lessened  in  intensity;  (b)  radia- 
tions are  brought  into  a  desired  direction  by  reflection  or 
refraction ;  (c)  radiations  are  changed  in  quality  by  selective 
absorption  in  the  material  of  the  globe. 

*  W.  E.  Sumpner,  Philosophical  Magazine,  35,  1893,  page  51.  Th. 
Stort,  Elektrotech.  Zeitschrift,  No.  32, 1895,  page  500  ;  given  in  abstract  in 
Electrical  Review  (London),  July  10,  1896,  page  37 ;  and  in  Electrical 
World,  26,  1895,  page  265. 

t  "  A  Photoinetrical  Comparison  of  Illuminating  Globes,"  R.  B.  Wil- 
liamson and  J.  H.  Klinck ;  a  paper  read  before  the  Electrical  Section  of 
the  Franklin  Institute,  March  21,  1899,  and  published  in  its  Journal,  Vol. 
149,  1900,  page  66. 

245 


246  APPENDIX 

The  source  of  light  employed  in  their  experiments  was  a 
Welsbach  burner,  and  the  action  of  the  globe  or  reflector  was 
studied  by  means  of  a  Bunsen  photometer.  The  change  in  the 
quality  of  the  light  by  selective  absorption  was  not  studied. 

The  action  of  such  globes  as  affect  the  quality  of  the  light, 
notably  opal  glass,  can  only  be  accurately  stated  when  their 
influence  on  the  quality  of  the  light  is  taken  into  account ;  and 
the  strictly  scientific  study  of  the  present  subject  would  entail 
complete  spectrophotometrical  measurements ;  but  when  it  is 
remembered  that  there  are  no  optical  standards  that  are  fol- 
lowed in  the  manufacture  of  the  globes,  and  that  any  commer- 
cial variety  varies  widely  in  its  action  on  the  transmitted  light, 
it  is  apparent  that  such  measurements  would  have  little  tech- 
nical value.  Any  data,  therefore,  presented  on  the  behaviour 
of  commercial  globes  toward  light  are  to  be  considered  as 
indicative  rather  than  conclusive. 

The  areas  included  by  the  curves  shown  in  the  illustrations 
were  determined  in  the  square-inch  unit  from  the  original 
curves,  and  the  mean  spherical  candle  power  was  calculated  by 
the  methods  already  explained  (page  41).  In  the  application 
of  these  curves  to  the  distribution  of  light  from  an  incandes- 
cent lamp,  it  must  be  remembered  that  the  test  light  was  a  gas 
flame,  and  that  the  curve  of  light  distribution  from  the  bare 
burner  greatly  differs  from  the  curve  of  distribution  from  an 
incandescent  lamp  (Fig.  50).  Care  must  also  be  exercised  to 
consider  the  incandescent  lamp  and  the  globe  or  reflector  to  be 
placed  in  relative  positions  equivalent  to  those  which  were 
used  in  these  tests. 

Two  similar  Welsbach  mantles  were  used:  one  was  main- 
tained in  a  fixed  position  as  a  standard,  and  its  illuminating 
power  was  repeatedly  checked ;  the  second  mantle  was  mounted 
on  a  traversing  arm,  the  burner  being  kept  vertical  in  all 
angular  positions  of  the  arm.  A  reflecting  mirror,  set  at  45°, 
was  attached  to  the  axis  of  the  bar,  which  was  adjusted  to 
lie  in  the  photometrical  axis  of  the  bench.  The  globes  and 
reflectors  were  tested  on  this  comparison  light. 


APPENDIX 


247 


I.   Holophane  globe  of  clear  glass  intended  for  the  horizontal  dis- 
tribution of  light,  Figure  63. 

CURVE  A,  WITHOUT  GLOBE 

Area  above  the  horizontal  axis        .        .        .        12.58 
Area  below  the  horizontal  axis        .        .        .        11.15 


HOLOPHANE 
t"=20  C.P. 
00 


7J. 


77 


IL 


£ 


v^.        00. 

FIG.  63. 

CURVE  B,  WITH  HOLOPHANE  GLOBE 

Area  above  the  horizontal  axis        .        .        .  7.92 

Area  below  the  horizontal  axis        .        .        .  12.72 

Efficiency            87% 

Mean  spherical  candle  power,  A      ...  46.46 

Mean  spherical  candle  power,  B  41.28 

The  holophane  globe  was  pear-shaped  and  ribbed  vertically 
on  the  interior,  and  horizontally  on  the  exterior,  surface.  The 
inner  ribs  were  all  similar  in  shape  with  a  sinusoidal  section, 
and  the  horizontal  ones  varied  with  their  location. 


248  APPENDIX 

II.   Ground  glass  globe  with  wide  flutings,  Figure  64. 


CURVE  A,  WITHOUT  GLOBE 


Area  above  the  horizontal  axis 
Area  below  the  horizontal  axis 


GROUND  GLOBE,   EGG  SHAPE  WIT*  WIDE  FLUTING8. 
1  =  20C.P. 

90 


12.40 
10.78 


FIG 


CURVE  B,  WITH  GROUND  GLASS  GLOBE 

Area  above  the  horizontal  axis         .         .        .  9.96 

Area  below  the  horizontal  axis        .        .        .  8.44 

Efficiency            79.3% 

Mean  spherical  candle  power,  A      ...  46.36 

Mean  spherical  candle  power,  B  36.80 

The  globe  was  egg-shaped  with  wide  shallow  flutings  on 
both  the  exterior  and  interior  surfaces.  Beyond  diminishing 
the  radial  intensity  of  the  light,  the  flux  above  the  horizontal 
plane  was  increased. 


APPENDIX 


249 


III.   Plain  opal  glass  globe,  Figure  65. 

CUR.VE    A,  WITHOUT    GLOBE 

Area  above  the  horizontal  axis 
Area  below  the  horizontal  axis 

PLAIN  OPAL  GLOBE  (EGG  SHAPE) 


12.40 
10.78 


FIG 


CURVE  B,  WITH  PLAIN  OPAL  GLASS  GLOBE 

Area  above  the  horizontal  axis         .         .         .  8.68 

Area  below  the  horizontal  axis        .         .         .  7.21 

Efficiency            68.5% 

Mean  spherical  candle  power,  A      ...  46.36 

Mean  spherical  candle  power,  B  31.78 

This  globe  was  also  egg-shaped  with  both  the  exterior  and 
the  interior  surfaces  plane.  There  is  a  marked  upward  dis- 
placement of  the  intensity  curve  as  well  as  large  absorption 
of  light,  with  consequent  low  efficiency. 


250  APPENDIX 

IV.   Slightly  opalescent  globe,  Figure  66. 

CURVE  A,  WITHOUT  GLOBE 

Area  above  the  horizontal  axis 
Area  below  the  horizontal  axis 


11.00 
9.60 


EGG  SHAPE  GLOBE  (LIGHT  OPALESCENT.) 
1  =  20  C.P. 
90 


FIG 


CURVE  B,  WITH  OPALESCENT  GLOBE 

Area  above  the  horizontal  axis        .         .         .  10.12 
Area  below  the  horizontal  axis         .         .        .          8.48 

Efficiency 90.2% 

Mean  spherical  candle  power,  A      ...  41.2 

Mean  spherical  candle  power,  B  .        .  37.2 

This,  too,  was  an  egg-shaped  globe  with  shallow  flutings 
arranged  spirally  on  one  surface  and  vertically  on  the  other. 
The  general  light  distribution  is  but  slightly  affected,  and  the 
absorption  is  very  low. 


APPENDIX 


251 


V.  Flat  opal  glass  reflector,  fluted,  Figure  67. 

CURVE  A,  WITHOUT  REFLECTOR 

Area  above  the  horizontal  axis 
Area  below  the  horizontal  axis 


OPAL  REFLECTOR 
1=  20  C.  P. 
90 


12.58 
11.15 


FIG.  67. 


CURVE  B,  WITH  OPAL  GLASS  REFLECTOR 

Area  above  the  horizontal  axis        .        .        .  6.41 

Area  below  the  horizontal  axis        .         .         .  14.20 

Efficiency            86.8% 

Mean  spherical  candle  power,  A              .        .  46.46 

Mean  spherical  candle  power,  B      .        .        .  41.22 

The  reflector  was  practically  flat  with  deep  radial  flutings. 
The  increase  in  the  intensity  beneath  the  horizontal  is  clearly 
shown ;  while  the  marked  loop  at  the  top  of  the  curve  is  due 
to  light  which  passed  through  the  large  opening  in  the  centre 
of  the  reflector. 


252  APPENDIX 

A  plain,  clear  glass  globe  did  not  alter  the  distribution  of 
the  light,  and  showed  an  efficiency  of  94.5  per  cent.  A  clear 
glass  globe  having  the  ordinary  pear-shaped  form,  and  made 
with  narrow  vertical  flutings,  gave  an  efficiency  of  86.6  per 
cent ;  while  another,  similarly  shaped,  but  having  narrow  ribs 
inside,  yielded  an  efficiency  of  91.5  per  cent ;  and  these  data 
may  probably  be  taken  for  the  working  limits  of  clear  glass 
globes. 

The  Welsbach  gas  burners  were  employed  as  the  light  source, 
for  experimental  reasons,  since  their  luminous  intensity  is 
fairly  constant  so  long  as  they  remain  intact,  provided  they 
are  allowed  to  burn  for  some  time  to  attain  a  normal  condi- 
tion. The  compared  lights  too,  being  similar  in  colour,  they 
gave  greater  precision  to  the  readings  of  the  Bunsen  screen. 

It  is  questionable  whether  the  results  of  these  experiments 
are  strictly  comparable  with  those  which  would  have  been 
obtained  had  the  light  source  more  nearly  agreed  in  quality 
with  that  of  the  electrical  arc.  The  selective  absorption  in 
the  globes,  especially  in  the  opalescent  and  opal  ones,  would 
doubtless  be  considerably  higher  with  the  bluer  arc  light. 
The  experimental  difficulties  when  using  the  arc  itself,  for 
such  tests,  are  very  great;  the  continual  change  in  the  light 
distribution  while  the  arc  is  burning,  due  to  the  shifting  posi- 
tion of  the  arc,  and  the  variation  of  its  potential  difference, 
are  obstacles  which  have  never  been  satisfactorily  overcome. 

Investigations  of  the  light-absorbing  power  of  globes  with 
the  arc  light  have  been  attempted,  however,  notably  by  Stort* 
and  Shepardson.f  The  arc  lamp  employed  by  Stort  was 
operated  with  a  current  intensity  of  10  amperes ;  and  by  the 
use  of  a  lens  and  screen,  the  length  of  the  arc  was  maintained 
at  2  millimetres;  the  positive  carbon  had  a  diameter  of  17, 
and  the  negative  one  of  10  millimetres.  The  values  which 
he  obtained  are  probably  too  small,  and  rather  underestimate 
the  screening  action  of  the  globes.  They  are :  — 

*  Th.  Stort,  reference  cited. 

t  G.  D.  Shepardson,  Electrical  World ;  23,  1894,  page  287. 


APPENDIX 


253 


LUMINOUS  INTENSITY  IN  CANDLES 

Maximum 
intensity 

Lower  mean 
hemispherical 
intensity 

Total  mean 
spherical 
intensity 

Loss  by  ab- 
sorption. 
Per  cent. 

Naked  light  .     .     . 
Clear  globes  . 
Frosted  globes  .     . 

1,161 
1,165 
654 

635 
606 
494 

362 
336 
320 

0 
6 
11 

Shepardson  found  that  the  distribution  of  the  light  was 
especially  disturbed  by  the  action  of  an  opal  or  white  glass 
globe.  Using  various  globes  and  comparing  the  intensity  of 
the  light  at  the  angle  of  maximum  intensity  for  the  bare  arc, 
he  found  that  a  clear  glass  globe  reduced  the  intensity  to  82 
per  cent,  a  ground  glass  globe  to  47  per  cent,  and  an  opal  glass 
globe  to  33  per  cent  of  the  value  of  the  illumination  from  the 
bare  arc. 

Such  results  naturally  follow  from  the  diffusing  action  of 
the  globes  on  the  light  given  from  the  arc,  which  is  much 
greater  than  their  absorption  of  the  light. 

The  photometrical  measurements  which  tests  of  this  charac- 
ter involve  are  necessarily  tedious,  and  they  require  that  the 
source  of  light  shall  remain  constant  throughout  the  tests. 
Doubtless  an  incandescent  lamp  operated  at  an  abnormally 
high  voltage  would  prove  a  more  satisfactory  source  of  light 
than  any  hitherto  employed,  and  the  quality  of  the  light  could 
be  made  to  approximate  closely  to  that  of  the  arc  light. 


B.    RECENT  INVESTIGATION  OF   LAMBERT'S  LAW  FOR 
THE  REFLECTION  OF  LIGHT 

Lambert's  law  of  the  cosines  has  been  simply  phrased  in 
the  text  (page  33)  to  meet  the  requirements  of  the  discussions 
and  applications  which  involve  this  principle.  A  more  ex- 
tended discussion  will  be  attempted  in  this  section. 


254  APPENDIX 

The  law  deals  with  secondary  sources  of  illumination  (page 
28),  and  is  a  fundamental  one  for  all  reflecting  screens.  In 
order  to  derive  a  general  expression  for  the  law,  consider  two 
diffusing  surfaces,  ^  and  8%  separated  by  a  distance  of  d 
units ;  these  surfaces  are  not  necessarily  planes,  but  may  have 
any  geometrical  character.  An  infinitesimal  area  ds1  is  taken 
on  the  surface  S^  and  similarly  ds2  on  S2 ;  and  being  so  small, 
they  will  be  regarded  as  plane  surfaces.  The  surface  Sl  is 
illuminated  by  a  light  source,  and  by  diffusion  emits  light  to 
the  second  surface  S2 ;  the  light  thus  is  emitted  from  St  and 
is  incident  upon  S2.  The  path  of  this  light  makes  an  angle  of 
emission  e,  with  the  normal  to  the  surface  element  ds^  and  an 
angle  of  incidence  i,  with  the  normal  to  the  surface  element 
ds2.  The  intrinsic  brightness  (page  32)  of  the  emitting  surface 
Si,  measured  normally,  will  be  taken  at  B  units,  and  the  quan- 
tity of  light  q,  which  finally  falls  on  the  surface  element 
ds2,  is 

jy 

q  =  —dsl  ds2  cos  c  cos  t, 

U2 

which  is  the  most  general  expression  for  Lambert's  law. 

Or,  one  surface,  S^  alone  may  be  considered,  which  receives 
from  a  light  source  an  illumination  whose  intensity  (page  30) 
measured  normally  is  /  units.  The  illumination  is  incident 
upon  the  surface  element  ds1?  at  an  angle  i,  and  the  diffused 
light  q  at  an  angle  of  emission  c  will  be 

q  —  Ids^  cos  c  cos  t.  (106) 

The  phenomenon  of  the  diffuse  reflection  of  light  is  entirely 
dependent  upon  the  character  of  the  reflecting  surface.  If 
this  contains  plane  surface  elements,  whose  size  is  a  magnitude 
which  is  large  in  comparison  with  the  dimensions  of  the  inci- 
dent light  wave,  a  certain  amount  of  regular  or  specular  reflec- 
tion (page  8)  will  occur,  associated  with  an  amount  of  diffused 
reflection;  and  the  regular  reflection  obeys  the  law  of  the 


APPENDIX  255 

equality  of  the  angles  of  incidence  and  reflection,  while  Lam- 
bert's law  would  apply  to  the  diffused  portion  of  the  reflected 
light.  The  smaller  the  grain  of  the  surface  becomes,  the  more 
closely  will  Lambert's  law  express  the  relations  between  the 
incident  and  the  emitted  light,  providing  this  law  precisely 
defines  the  phenomenon. 

The  efforts  of  later  investigators  of  the  validity  of  this  law 
have  been  especially  directed  toward  the  production  of  a  suffi- 
ciently fine-grained  surface  to  insure  complete  diffusion  of  the 
light  and  eliminate  all  regular  reflection.  A  surface  of  this 
nature  is  properly  called  a  "matt"  surface.  In  the  last 
analysis  all  light  waves  are  reflected  regularly,  however  small 
the  grain  of  the  surface ;  and  the  distinction  between  diffuse 
and  specular  reflection  is  one  wholly  of  direction.  In  the  case 
of  specular  reflection  a  considerable  quantity  of  light  is  re- 
flected in  a  particular  direction ;  when  diffuse  reflection  occurs, 
the  quantities  of  light  specularly  reflected  from  the  surface 
elements  are  very  small,  for  the  planes  of  the  elements  will 
likely  be  so  disposed  with  reference  to  each  other  that  their 
normals  will  radiate  in  all  directions  with  considerable  uni- 
formity ;  the  result  would  be  that  no  measurable  quantity  of 
reflected  light  would  have  a  defined  direction. 

Wright  *  attempted  to  produce  a  matt  surface  by  compress- 
ing powders  in  steel  moulds  into  coherent  blocks  under  press- 
ures of  4  to  20  tons.  He  found  no  evidence  of  normal  reflection 
occurring  from  the  surfaces  thus  prepared,  and  he  considered 
them  properly  matt  surfaces.  Amongst  other  materials  com- 
pressed and  tested,  he  used  carbonate  of  magnesium  and  plas- 
ter of  Paris ;  and  he  observed  that  the  size  of  the  particles  was 
not  changed  by  the  compression  to  which  they  were  subjected. 
The  fact  that  he  could  detect  no  polarization  of  the  light  upon 
reflection  was  taken  as  the  evidence  that  no  normal  reflec- 


*  H.  R.  Wright,  "Photometry  of  the  Diffuse  Reflexion  of  Light  on  Matt 
Surfaces,"  Philosophical  Magazine,  February,  1900,  page  199 ;  the  paper 
gives  an  excellent  summary  of  the  investigations  of  Lambert's  law. 


256  APPENDIX    ' 

tion  of  the  light  had  taken  place.  A  matt  surface  properly 
defined  is  one  which  entirely  diffuses  the  light  reflected  from  it 
without  polarization,  or  specular  reflection.  Specular  reflection 
detected  from  surfaces  supposed  to  be  matt  ones,  would  indicate 
that  the  reflecting  areas  of  the  particles  were  large  relative  to 
the  dimensions  of  the  light  waves,  or  that  a  peculiarly  orderly 
arrangement  of  exceedingly  minute  surface  planes  had  occurred. 
As  the  latter  is  improbable,  the  absence  of  specularly  reflected, 
or  polarized  light  is  apparently  sufficient  evidence  of  the  matt 
character  of  the  surface. 

The  conclusions  at  which  Wright  arrived  from  his  experi- 
ments were :  — 

1.  "  Common  light  is  not  polarized  by  diffuse  reflection. 

2.  "  The  intensity  of  the  light  diffusely  reflected  under  the 
angles  -f  €  and  —  e  is  the  same,  or  it  is  independent  of  the  azi- 
muth.    There  is  no  specular  reflection. 

3.  "  The  law  of  emission  by  constant  incidence  is  indepen- 
dent of  colour,  or  the  coefficient  of  diffusion  is  independent  of 
the  wave  length  in  the  case  of  particles  of  the  given  size. 

4.  "  A  law  for  the  intensity  of  reflected  scattered  light  can 
not  be  symmetrical  in  reference  to  the  angles  t  and  e. 

5.  "The  intensity  of  the  diffuse  reflected  light  with  the 
angle  e  constant  and  with  varying  angles  of  incidence  i,  is  not 
proportional  to  the  cosine  i,  as  Lambert  assumes. 

6.  "The  intensity  of  the  diffuse  reflected  light  with  the 
angle  i  constant  and  the  angle  €  varying,  is  proportional  to  the 
cosine  e,  or  Lamberts  law  of  emanation  is  strictly  correct  for 
absolutely  matt  surfaces  without  any  exception. 

7.  "  The  so-called  (  law  of  the  cosine '  (q  =  T2ds  •  cos  t  cos  e) 
is  not  true  in  consequence  of  the  deviations  of  the  law  of  the 
cosine  t.     The  deviations  range  between  4.6  per  cent  and  10 
per  cent." 

From  considerations  of  the  geometrical  character  of  truly 
matt  surfaces,  it  is  probable  that  the  quantity  of  light  emitted 
is  not  strictly  a  function  of  the  cosine  e. 


APPENDIX  257 

These  considerations  are  of  great  importance  in  their  rela- 
tion to  diffusing  plates  employed  in  such  photometers  as  the 
Lummer-Brodhun  and  the  Leonhard  Weber ;  and  there  is  need 
of  marked  improvement  in  the  surfaces  of  the  plates  usually 
provided.  They  also  emphasize  the  necessity  for  the  symmet- 
rical adjustment  of  the  Lummer-Brodhun  sight  box  regarding 
the  angles  of  the  incident  and  emitted  rays. 


258  APPENDIX 


C.    TABLE  OF   RATIOS   FOR   A   100-FART   PHO- 
TOMETER  BAR* 

The  formula  for  the  calculation  of  the  intensity  of  a  com- 
pared light  by  use  of  this  table  of  ratios,  is  : 


in  which  Ie  is  the  light  intensity  sought,  and  /,  that  of  the 
standard  light,  while  the  value  of  the  ratio  P,  is  taken  from 
the  table,  corresponding  to  the  observed  scale  reading. 

Thus,  if  the  screen  is  set  at  a  distance  of  40.6  units  from  the 
standard  light,  the  ratio  for  this  scale  reading  is  2.14,  and  if 
J.  has  a  value  of  14.5  light  units, 

Ic  =  2.14  x  14.5 

=  31.03  light  units. 
*  W.  L.  Smith,  Technology  Quarterly,  1896,  page  60. 


APPENDIX 


259 


Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

.10 

75.97 

.47 

59.33 

.84 

52.18 

1.21 

47.62 

1.58 

44.31 

.11 

75.09 

.48 

59.07 

.85 

52.03 

1.22 

47.51 

1.59 

44.23 

.12 

74.27 

.49 

58.82 

.86 

51.88 

1.23 

47.41 

1.60 

44.15 

.13 

73.50 

.50 

58.57 

.87 

51.74 

1.24 

47.31 

1.61 

44.08 

.14 

72.77 

.51 

58.34 

.88 

51.60 

1.25 

47.21 

1.62 

44.00 

.15 

72.08 

.52 

58.10 

.89 

51.46 

1.26 

47.11 

1.63 

43.92 

.16 

71.43 

.53 

57.87 

.90 

51.32 

1.27 

47.01 

1.64 

43.85 

.17 

70.81 

.54 

57.64 

.91 

51.18 

1.28 

46.92 

1.65 

43.77 

.18 

70.21 

.55 

57.42 

.92 

51.04 

1.29 

46.82 

1.66 

43.70 

.19 

69.64 

.56 

57.20 

.93 

50.90 

1.30 

46.72 

1.67 

43.62 

.20 

69.10 

.57 

56.98 

.94 

50.77 

1.31 

46.63 

1.68 

43.55 

.21 

68.58 

.58 

56.77 

.95 

50.64 

1.32 

46.54 

1.69 

43.48 

.22 

68.07 

.59 

56.56 

.96 

50.51 

1.33 

46.44 

1.70 

43.41 

.23 

67.58 

.60 

56.35 

.97 

50.38 

1.34 

46.35 

1.71 

43.33 

.24 

67.12 

.61 

56.15 

.98 

50.25 

1.35 

46.26 

1.72 

43.26 

.25 

66.66 

.62 

55.95 

.99 

50.12 

1.36 

46.16 

1.73 

43.19 

.26 

66.23 

.63 

55.75 

1.00 

50.00 

1.37 

46.07 

1.74 

43.12 

.27 

65.81 

.64 

55.55 

1.01 

49.88 

.38 

-  45.98 

1.75 

43.05 

.28 

65.40 

.65 

55.36 

1.02 

49.76 

.39 

45.89 

1.76 

42.98 

.29 

65.00 

.66 

55.17 

1.03 

49.63 

.40 

45.80 

1.77 

42.91 

.30 

64.61 

.67 

54.98 

1.04 

49.51 

.41 

45.72 

1.78 

42.84 

.31 

64.24 

.68 

54.80 

1.05 

49.39 

.42 

45.63 

1.79 

42.77 

.32 

63.87 

.69 

54.62 

1.06 

49.27 

1.43 

45.54 

1.80 

42.70 

.33 

63.51 

.70 

54.44 

1.07 

49.15 

1.44 

45.45 

1.81 

42.64 

.34 

63.17 

.71 

54.27 

1.08 

49.04 

1.45 

45.37 

1.82 

42.57 

.35 

62.83 

.72 

54.10 

1.09 

48.93 

1.46 

45.28 

1.83 

42.50 

.36 

62.50 

.73 

53.93 

1.10 

48.81 

1.47 

45.20 

1.84 

42.44 

.37 

62.18 

.74 

53.76 

1.11 

48.70 

1.48 

45.12 

1.85 

42.37 

.38 

61.86 

.75 

53.59 

1.12 

48.59 

1.49 

45.03 

1.86 

42.30 

.39 

61.55 

.76 

53.42 

1.13 

48.48 

1.50 

44.95 

1.87 

42.24 

.40 

61.25 

.77 

53.26 

1.14 

48.36 

1.51 

44.87 

1.88 

42.18 

.41 

60.97 

.78 

53.10 

1.15 

48.25 

1.52 

44.79 

1.89 

42.11 

.42 

60.68 

.79 

52.94 

1.16 

48.14 

1.53 

44.71 

1.90 

42.04 

.43 

60.39 

.80 

52.78 

1.17 

48.04 

1.54 

44.62 

1.91 

41.98 

.44 

60.12 

.81 

52.63 

1.18 

47.93 

1.55 

44.54 

1.92 

41.92 

.45 

59.85 

.82 

52.48 

1.19 

47.83 

1.56 

44.47 

1.93 

41.85 

.46 

59.58 

.83 

52.33 

1.20 

47.72 

1.57 

44.39 

1.94 

41.79 

260 


APPENDIX 


Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

1.95 

41.73 

2.64 

38.10 

3.38 

35.23 

5.05 

30.79 

6.90 

27.57 

1.96 

41.67 

2.66 

38.01 

3.40 

35.16 

5.10 

30.69 

6.95 

27.50 

1.97 

41.61 

2.68 

37.92 

3.42 

35.10 

5.15 

30.59 

7.00 

27.43 

1.98 

41.55 

2.70 

37.83 

3.44 

35.03 

5.20 

30.49 

7.05 

27.36 

1.99 

41.48 

2.72 

37.75 

3.46 

34.97 

5.25 

30.38 

7.10 

27.29 

2.00 

41.42 

2.74 

37.66 

3.48 

34.90 

5.30 

30.28 

7.15 

27.22 

2.02 

41.30 

2.76 

37.58 

3.50 

34.83 

5.35 

30.18 

7.20 

27.15 

2.04 

41.18 

2.78 

37.49 

3.55 

34.67 

5.40 

30.09 

7.25 

27.08 

2.06 

41.06 

2.80 

37.41 

3.60 

34.51 

5.45 

29.99 

7.30 

27.01 

2.08 

40.95 

2.82 

37.32 

3.65 

34.36 

5.50 

29.89 

7.35 

26.95 

2.10 

40.83 

2.84 

37.24 

3.70 

34.21 

5.55 

29.80 

7.40 

26.88 

2.12 

40.72 

2.86 

37.16 

3.75 

34.05 

5.60 

29.70 

7.45 

26.81 

2.14 

40.60 

2.88 

37.08 

3.80 

33.90 

5.65 

29.61 

7.50 

26.75 

2.16 

40.49 

2.90 

37.00 

3.85 

33.76 

5.70 

29.52 

7.55 

26.69 

2.18 

40.38 

2.92 

36.92 

3.90 

33.62 

5.75 

29.43 

7.60 

26.62 

2.20 

40.27 

2.94 

36.84 

3.95 

33.47 

5.80 

29.34 

7.65 

26.55 

2.22 

40.16 

2.96 

36.76 

4.00 

33.33 

5.85 

29.25 

7.70 

26.49 

2.24 

40.05 

2.98 

36.68 

4.05 

33.19 

5.90 

29.16 

7.75 

26.43 

2.26 

39.95 

3.00 

36.60 

4.10 

33.06 

5.95 

29.07 

7.80 

26.37 

2.28 

39.84 

3.02 

36.53 

4.15 

32.92 

6.00 

28.99 

7.85 

26.30 

2.30 

39.74 

3.04 

36.45 

4.20 

32.79 

6.05 

28.90 

7.90 

26.24 

2.32 

39.63 

3.06 

36.37 

4.25 

32.66 

6.10 

28.82 

7.95 

26.18 

2.34 

39.53 

3.08 

36.30 

4.30 

32.54 

6.15 

28.74 

8.00 

26.12 

2.36 

39.43 

3.10 

36.23 

4.35 

32.41 

6.20 

28.66 

8.05 

26.06 

2.38 

39.33 

3.12 

36.15 

4.40 

32.28 

6.25 

28.58 

8.10 

26.00 

2.40 

39.23 

3.14 

36.08 

4.45 

32.16 

6.30 

28.49 

8.15 

25.94 

2.42 

39.13 

3.16 

36.01 

4.50 

32.04 

6.35 

28.41 

8.20 

25.88 

2.44 

39.03 

3.18 

35.93 

4.55 

31.92 

6.40 

28.33 

8.25 

25.82 

2.46 

38.93 

3.20 

35.86 

4.60 

31.80 

6.45 

28.25 

8.30 

25.77 

2.48 

38.84 

3.22 

35.79 

4.65 

31.68 

6.50 

28.17 

8.35 

25.71 

2.50 

38.75 

3.24 

35.72 

4.70 

31.57 

6.55 

28.09 

8.40 

25.65 

2.52 

38.65 

3.26 

35.64 

4.75 

31.45 

6.60 

28.01 

8.45 

25.60 

2.54 

38.55 

3.28 

35.57 

4.80 

31.34 

6.65 

27.94 

8.50 

25.54 

2.56 

38.46 

3.30 

35.50 

4.85 

31.22 

6.70 

27.87 

8.55 

25.48 

2.58 

38.37 

3.32 

35.44 

4.90 

31.12 

6.75 

27.79 

8.60 

25.43 

2.60 

38.28 

3.34 

35.37 

4.95 

31.01 

6.80 

27.72 

8.65 

25.37 

2.62 

38.19 

3.36 

35.30 

5.00 

30.90 

6.85 

27.64 

8.70 

25.32 

APPENDIX 


261 


Ratio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

8.75 

25.27 

9.65 

24.35 

12.75 

21.88 

17.25 

19.39 

23.50 

17.10 

8.80 

25.21 

9.70 

24.30 

13.00 

21.71 

17.50 

19.28 

24.00 

16.95 

8.85 

25.16 

9.75 

24.26 

13.25 

21.55 

17.75 

19.18 

24.50 

16.81 

8.90 

25.10 

9.80 

24.21 

13.50 

21.39 

18.00 

19.07 

25.00 

16.67 

8.95 

25.05 

9.85 

24.17 

13.75 

21.24 

18.25 

18.97 

25.50 

16.53 

9.00 

25.00 

9.90 

24.12 

14.00 

21.09 

18.50 

18.86 

26.00 

16.40 

9.05 

24.95 

9.95 

24.07 

14.25 

20.94 

18.75 

18.76 

26.50 

16.27 

9.10 

24.90 

10.00 

24.03 

14.50 

20.80 

19.00 

18.66 

27.00 

16.14 

9.15 

24.85 

10.25 

23.80 

14.75 

20.66 

19.25 

18.56 

27.50 

16.01 

9.20 

24.79 

10.50 

23.58 

15.00 

20.52 

19.50 

18.46 

28.00 

15.89 

9.25 

24.74 

10.75 

23.37 

15.25 

20.39 

19.75 

18.37 

28.50 

15.78 

9.30 

24.69 

11.00 

23.17 

15.50 

20.26 

20.00 

18.28 

29.00 

15.66 

9.35 

24.64 

11.25 

22.97 

15.75 

20.13 

20.50 

18.09 

29.50 

15.55 

9.40 

24.60 

11.50 

22.77 

16.00 

20.00 

21.00 

17.91 

30.00 

15.45 

9.45 

24.55 

11.75 

22.57 

16.25 

19.88 

21.50 

17.74 

9.50 

24.50 

12.00 

22.40 

16.50 

19.75 

22.00 

17.57 

9.55 

24.45 

12.25 

22.23 

16.75 

19.63 

22.50 

17.41 

9.60 

24.40 

12.50 

22.05 

17.00 

19.51 

23.00 

17.25 

Eatio 

Scale 

Eatio 

Scale 

Eatio 

Scale 

Ratio 

Scale 

Eatio 

Scale 

31 

15.23 

43 

13.23 

60 

11.43 

90 

9.54 

150 

7.55 

32 

15.02 

44 

13.10 

62 

11.27 

95 

9.31 

155 

7.44 

33 

14.83 

45 

12.97 

64 

11.11 

100 

9.09 

160 

7.33 

34 

14.64 

46 

12.85 

66 

10.96 

105 

8.89 

165 

7.22 

35 

14.46 

47 

12.73 

68 

10.82 

110 

8.70 

170 

7.12 

36 

14.28 

48 

12.61 

70 

10.67 

115 

8.53 

175 

7.03 

37 

14.12 

49 

12.50 

72 

10.54 

120 

8.36 

180 

6.94 

38 

13.96 

50 

12.39 

74 

10.41 

125 

8.21 

185 

6.85 

39 

13.80 

52 

12.18 

76 

10.29 

130 

8.06 

190 

6.77 

40 

13.65 

54 

11.98 

78 

10.17 

135 

7.92 

195 

6.68 

41 

13.51 

56 

11.79 

80 

10.06 

140 

7.79 

200 

6.60 

42 

13.37 

58 

11.61 

85 

9.79 

145 

7.67 

INDEX  TO  SUBJECTS 


THE  NUMBERS  REFER  TO  THE  PAGE 


Absorption  of  light  by  mirrors,  235. 

Absorption  plates,  100. 

Absorption,  selective,  8. 

Acetylene  gas,  194;  as  a  light  stand- 
ard, 195. 

Actinometer,  103. 

Alternating  current  arc,  mean  spheri- 
cal intensity,  42. 

Ammeter,  sensitiveness,  202. 

Amyl  acetate,  as  a  combustible,  148; 
tests  for  purity,  149. 

Amyl  acetate  flame,  influence  of  car- 
bon dioxide,  156 ;  of  pressure,  157 ;  of 
humidity,  154. 

Amyl  acetate  lamp,  145 ;  value  in 
candle  power,  170;  directions  for 
use,  159;  reproducibility,  153;  col- 
our of  flame,  152;  flame  height,  152 ; 
influence  of  temperature  on,  153; 
the  wick,  150;  the  wick  tube,  151. 

Aperture,  effect  of  small,  131. 

Arc,  alternating  current,  225;  light 
distribution,  228. 

Arc,  continuous  current,  160;  light 
distribution,  226. 

Arc,  electrical,  intrinsic  brightness 
independent  of  power  absorbed,  162 ; 
space  distribution  of  illumination, 
226 ;  maximum  intensity,  227 ;  radial 
intensity  as  a  cosine  function,  228; 
function  between  horizontal  and 
maximum  intensities,  231. 

Arc,  electrical,  source  of  illuminating 
power,  161 ;  luminosity,  222 ;  quality 
of  light,  221 ;  its  constitution,  222 ; 


its  behaviour,  223 ;  temperature  of, 
161 ;  enriching  by  hydrocarbons,  222. 

Arc,  enclosed,  229 ;  effect  of  enclosure, 
230  ;  shape  of  carbon  tips,  223. 

Arc  lamp,  characteristics,  224;  sus- 
pension for,  236. 

Arc  lamp  photometry,  220 ;  practice 
of,  232 ;  difficulties  of,  220 ;  candle- 
power  ratings,  220. 

Arc  light,  efficiency,  232. 

Arc  light  photometry,  224;  criterion 
for,  232 ;  calculations,  241 ;  general 
details,  241  ;  adjustments,  239;  ar- 
rangement of  photometer  train,  237 ; 
sensitiveness  of  setting,  239  ;  trav- 
ersing the  arc,  237;  standard  light 
for,  233;  calibration  of  standard 
incandescent  lamp,  234;  size  of 
standard  incandescent  lamp,  235; 
use  of  high-power  standards,  240. 

Arc,  standard  of  light,  160;  Blondel's, 
162. 

Argand  gas  flames,  194. 

Atmospheric  pressure,  effect  on  lu- 
minosity of  flames,  114. 


Bar,    photometer,    proper     working 

length,  207. 

Bench,  photometer,  46, 104. 
Benzine  lamp,  194. 
Benzine  standard  of  light,  81. 
Bolometer,  103. 
Bougie  decimale,  170. 
Brightness,  intrinsic,  of  a  light  source, 

31. 


263 


264 


INDEX 


Bunsen  photometer,  52. 

Bunsen  screen,  78 ;  theory  of,  66 ;  its 

sensitiveness,   69;    preparation   of, 

65 ;  its  practice,  68. 


Candle,  decimal,  170;  Munich,  123; 
Star,  123,  162. 

Candle,  English,  115;  combustible, 
117;  the  wick,  117;  normal  flame 
height,  118, 170  ;  influence  of  press- 
ure, 120;  quality  of  light,  115; 
B.  A.  report  on,  115 ;  specifications 
for,  116 ;  requirements  for  unit  light, 
120 ;  light  value,  170. 

Candle-foot  unit,  98. 

Candle,  German,  121;  behaviour  of, 
123;  combustible  and  wick,  122; 
quality  of  light,  122 ;  normal  flame 
height,  122,  170 ;  light  value  of,  170. 

Candle-meter  unit,  37,  99. 

Candle,  paraffine,  121. 

Candle  power  scale,  106. 

Candle  power,  the  unit,  37 ;  discussion 
of  the  term,  34;  objections  to  the 
term,  158. 

Candle,  standard,  112;  directions  for 
use,  120. 

Canopy  for  lights  and  screen,  201. 

Carbon,  emissivity  of,  221 ;  tempera- 
ture of  ebullition,  161 ;  vaporization 
from  incandescent  lamp  filaments, 
176. 

Carbon,  graphitic  on  incandescent  fila- 
ments, 172. 

Carbon,  the  quality  influencing  the 
arc  light,  161, 163. 

Carbons,  arc  lamp,  221 ;  pointing  of, 
222. 

Carburetting  the  gas,  129. 

Carcel  lamp,  123;  dimensions,  124; 
the  combustible,  124;  the  wick  and 
flame  height,  125 ;  as  unit  light,  34 ; 
factors  of  variation,  126. 

Characteristics  of  the  arc  lamp,  224; 
of  the  incandescent  lamp,  183. 

Chemical  photometry,  103. 

Chimneys,  reflection  caused  by,  131. 

Colour  brightness  of  surfaces,  26. 

Colour  curves,  13,  14. 

Colour  groups  in  spectrum,  7. 


Colour  vision,  theory  of,  12,  13. 

Coloured  lights,  photometry  of,  92. 

Colour,  physiological  meaning,  12; 
physical  meaning,  6 ;  perception  of, 
20 ;  theory  of,  13. 

Colza-oil,  124, 193. 

Comparison  lamps  for  arc  light  pho- 
tometry, 232. 

Complementary  colours,  17;  by  fa- 
tigue, 213. 

Conroy  screen,  61. 

Constants  of  Weber  photometer,  87. 

Contrast  of  colours,  exaggerated,  18. 

Contrast  principle,  76. 

Contrast  train  of  Lummer-Brodhun 
photometer,  78. 

Contrasts,  method  of  similar,  77;  in 
Bunsen  screen,  68. 

Crater,  positive  as  a  source  of  light, 
227. 

D 

Diffused  reflection,  254. 

Diffusing  plates,  wedge-shaped,  89. 

Diffusing  screens,  48. 

Diffusion,  selective,  9. 

Disk,  rotating  sector,  principle  of,  24. 

Dispersion  lens,  100. 

Distance,  law  of,  30. 

Distribution  of  light,  from  a  small 
source,  29;  about  an  incandescent 
lamp,  41 ;  an  arc  lamp,  41. 

Duration  period  of  vision,  21 ;  a  func- 
tion of  colour  and  exposure,  22. 


Edgerton  photometer,  193. 

Efficiency  of  arc  light,  232. 

Electromotive  force,  source  best 
adapted  for  photometrical  tests,  202. 

Elster  diffusing  screen,  61,  90. 

Emission  of  light  from  filament,  rate 
of,  173. 

Emissivity  defined,  11;  superficial,  12. 

Emissivity  of  carbon  in  the  arc,  221. 

Emissivity  of  incandescent  filament, 
172;  affected  by  character  of  sur- 
face, 172 ;  changed  by  repeated  heat- 
ing, 174. 

Eye,  the,  as  a  photometer,  2. 

Eye,  fatigue  of,  17. 


INDEX 


265 


Factor,  the  personal,  210. 

Fatigue  of  the  eye,  17,  212, 

Fechner's  law  of  sensation,  15,  110, 
111 ;  in  illumination,  19. 

Filament  for  incandescent  lamps,  the 
cellulose,  185 ;  details  of  manufac- 
ture, 185 ;  flashing,  186 ;  comparison 
of  flashed  and  unflashed,  177. 

Filaments,  incandescent  lamp,  surface 
of,  171;  their  comparableness,  181; 
emissivity  from,  172 ;  temperature  of 
incandescence,  174;  efficiency  rela- 
tions, 178;  unit  surface  radiation, 
173. 

Flame  gauge,  Kriiss  optical,  147. 

Flame  height  and  illuminating  power, 
114 ;  normal  for  English  candle,  118 ; 
for  German  caudle,  122. 

Flame,  standard,  precautions  in  use, 
213. 

Flames,  their  constitution,  113;  lumi- 
nosity of,  112 ;  influence  of  air  cur- 
rents on,  118. 

Flashing  of  the  filament,  171. 

Flicker  photometer,  87,  19,  232,  234. 

Franklin  Institute  tests,  205. 


Gas,    illuminating,    deteriorating   in 

contact  with  water,  136. 
Gauge,  test,  for  amyl  acetate  lamp, 

148. 

Glass,  opal,  diffusing  screen,  61. 
Globes,  absorption  of  light  by,  245. 
Globes,  clear  glass,  252 ;  ground  glass, 

248 ;    holophane,    247  ;    opal   glass, 

249 ;  opalescent,  250. 
Graduation  of  photometer  bar,  207. 


Harcourt  standard  of  light,  132. 

Hefner  lamp,  145  ;  report  of  A.  I.  E.  E. 
on,  148. 

Hefner  unit,  value  of,  158;  in  terms 
of  candle  power,  170;  the  term  dis- 
cussed, 36;  as  a  substitute  for  the 
term  "  candle  power,"  158. 


ilemispherical  intensity,  mean,  43. 
Solders  for  incandescent  lamp,  204; 

rotating,  206. 
3olophane  globe,  247. 
Hysteresis  of  resistance  of  filament, 

175,  189. 

I 

Illuminating  intensity,  the  unit,  31. 

[lluminating  power,  practical  unit,  34, 
112 ;  a  function  of  flame  height,  114. 

fllumination  change  of  movement  of 
screen,  210. 

Illumination,  discussion,  19;  physical 
basis  for,  20;  distinguished  from 
illuminating  power,  109;  defined  in 
terms  of  energy,  102 ;  smallest  per- 
ceptible change,  16. 

Illumination  photometer,  95. 

Illuminometer  of  Houston  and  Ken- 
nelly,  98. 

Incandescent  filament,  temperature 
of,  174. 

Incandescent  filament  as  a  primary 
standard  of  light,  187 ;  B.  A.  unit, 
187 ;  failure  of,  188. 

Incandescent  lamp,  171 ;  absorption  of 
light  in,  179;  life  characteristics, 
183 ;  tests  and  data,  182 ;  light  distri- 
bution, 196 ;  centring  on  bench,  214; 
spinning,  215;  functions  between 
intensity  of  light  and  electrical  prop- 
erties, 179, 181,  203;  potential  sensi- 
tiveness, 204 ;  magnitude  of  errors  in 
measurement  of,  190;  sensitiveness 
of  measurements,  191. 

Incandescent  lamp  as  a  comparison 
or  working  standard,  189,  192 ;  con- 
stancy of ,  190;  working  conditions, 
191 ;  precautions  for,  191,  213. 

Incandescent  lamp  photometry,  209; 
calculations,  216;  electromotive  force 
for,  202;  sensitiveness  of  electrical 
instruments,  204;  spherical  inten- 
sity, 216. 

Inclination  of  the  screen,  51. 

Intensity,  mean  spherical,  38. 

Intensity  of  illumination,  unit,  and 
general  law,  31. 

Intrinsic  brightness  of  a  light  source, 
31. 


266 


INDEX 


Jet  gas  flames,  194. 

Joly  diffusing  screen,  78,  90. 


Keats  lamp,  193. 

Kriiss  optical  flame  gauge,  147. 


Lambert  photometer,  56;  screen,  101; 
translucent  screen,  57. 

Lambert's  law,  33,  96 ;  recent  investi- 
gation of,  253. 

Law  of  inverse  squares,  130;  of  in- 
clination of  illuminating  surface,  32. 

Light  change,  least  observable,  50. 

Light,  quantitative  judgment  of,  14; 
duration  of  retinal  impression,  21; 
reflection  from  surfaces,  20 ;  visible, 
6 ;  intensity  for  distinct  vision,  37. 

Light  screen,  errors  of,  130. 

Light  sources,  primary  and  secondary, 
109;  intensity  of  powerful  sources, 
241. 

Light  standards,  working  value  of, 
169 ;  sources  of  error,  157. 

Light  unit  as  a  term,  37. 

Lights,  proper  conditions  for  compar- 
ing, 18. 

Luminosity  of  flames,  112;  effect  of 
moisture  on,  114 ;  of  pressure,  113. 

Lummer-Brodhun  photometer,  70,  71, 
257;  adjustments,  72;  advantages 
and  faults  of,  77;  working  direc- 
tions, 77. 

Lummer-Brodhun  screen,  212, 232, 234, 
242;  contrast  prism,  80. 


M 

Matt  surfaces,  255. 

Mean  spherical  intensity,  38;  of  arc 
light,  231. 

Measurement,  general  law,  1. 

Methven  screen,  126,  137  ;  its  develop- 
ment, 127 ;  report  on,  137. 

Mirrors,  coefficient  for,  236;  calibra- 
tion of,  235 ;  correction  factor,  236. 

Mirrors  for  Bunsen  screen,  63. 


Mirrors  for  arc  light  photometry,  235. 

Moisture,    effect    on    luminosity    of 

flames,  114 ;  of  candle  flame,  119. 

N 

Netherlands  Commission,  100;  report 
on  light  standards,  144. 

Nichols-Ritchie  screen,  55. 

Nomenclature  of  photometrical  quan- 
tities, 33. 

O 

Opal  glass  diffusing  screen,  48. 
Optical  flame  gauge,  Kriiss,  147. 
Optical  screen,  70. 
Optics,  physiological,  12. 


Paraffine  diffusion  screen,  61. 

Pentane  air-gas  standard,  132. 

Pentane  flame,  radiant  centre,  141; 
influence  of  humidity  and  pressure, 
142. 

Pentane  lamp,  137  ;  the  combustible, 
132;  the  wick,  137;  flame  height, 
140 ;  production  of  flame,  137 ;  colour 
of  flame,  140 ;  heating  effects,  137  ; 
as  a  standard  of  light,  143;  light 
value  of,  170. 

Pentane  lamp,  the  ten-candle,  138; 
directions  for  use,  139. 

Pentane  standard,  132;  the  burner, 
133;  colour  of  flame,  134;  tests  of, 
134;  improvements  in,  135;  reports 
on,  134,  135. 

Persistence  interval  of  vision,  19. 

Persistence  of  vision,  24 ;  effects  of,  18. 

Personal  factor  in  photometry,  210. 

Petroleum  burning  lamps,  193. 

Photometer  bar,  proper  working 
length,  207 ;  graduation  of,  207. 

Photometer  bench,  46,  104  ;  mounting 
of,  200. 

Photometer,  essential  elements  of  the, 
46;  the  ideal,  2;  illumination  types, 
95;  the  dispersion,  100;  Ayrton  and 
Perry,  100 ;  Bouguer,  52 ;  Bunsen, 
62 ;  Conroy,  58 ;  flicker,  91 ;  Foucault, 
56;  Lummer-Brodhun,  70;  Preece 
and  Trotter,  95;  Queen  portable,  218; 


INDEX 


267 


Ritchie,  55,  56;  Rood,  04;  Rumford, 
53 ;  Thompson,  60 ;  Leonhard  Weber, 
78. 

Photometer  room,  and  apparatus,  198 ; 
dimensions  for,  199;  for  arc  light 
photometry,  238. 

Photometer  table,  wiring  plan,  200. 

Photometrical  data,  their  contradic- 
tory character,  168. 

Photometrical  law,  the  generalized, 
32,54. 

Photometrical  quantities,  28;  their 
nomenclature,  33. 

Photometrical  skill  required,  213. 

Photometrical  standards,  basis  for, 
110. 

Photometry,  denned,  1,  46 ;  basis  for, 
45;  direct  purposes  of,  47;  present 
tendencies  in,  45. 

Photometry  of  differently  coloured 
lights,  86. 

Physical  principles  of  photometry,  4. 

Platinum  standard  of  light,  the  incan- 
descent, 164;  Reichsanstalt's  tests, 
167. 

Polarization  of  light,  256. 

Polish,  influence  on  emissivity,  11. 

Portable  photometers,  the  Queen,  218. 

Practical  apparatus,  observations  on, 
218. 

Practical  unit  of  illuminating  power, 
34. 

Primary  and  secondary  light  sources, 
109. 

Primary  sources  of  illumination  de- 
nned, 28. 

Prisms,  totally  reflecting,  10,  56,  78. 

Purkinje  effect,  26. 


Quantity  of  light,  law  of  variation  with 
the  distance,  30. 

R 

Radiant  centre,  of  flame,  131 ;  of  pen- 

tane  flame,  141. 

Radiometer  as  a  photometer,  103. 
Ratio  scale,  208. 

Ratios  for  photometer  bar,  table,  258. 
Reading  lamp  for  sight  box,  200. 


Reflecting  screen,  47. 

Reflection  angle  for  inclined  screen,  60. 

Reflection  of  light,  total,  9 ;  diffused 
and  regular,  8,  254;  from  various 
surfaces,  10. 

Reflectors,  action  of,  245;  opal  glass, 
251. 

Reichsanstalt,  certificate  for  Hefner 
lamp,  158 ;  standard  lamp,  145 ;  pho- 
tometer, 70 ;  photometer  bench,  104. 

Report,  B.  A.  on  amyl  acetate  lamp, 
148. 

Resistance,  temperature  change  of,  in 
filament,  175 ;  hysteresis  change  of, 
175. 

Retina,  duration  of  light  impression 
on,  21. 

Rheostat  for  incandescent  lamp  pho- 
tometry, 201. 

Ritchie  photometer,  62 ;  wedge-shaped 
screen,  58,  60,  92. 

Rood  flicker  photometer,  94. 

Rotators  for  incandescent  lamp,  206. 

Riidorff  mirrors,  63. 


8 

Sabine  wedge,  89. 

Scale,  equally  divided,  207;  propor- 
tional, 207;  the  ratio,  208;  calcula- 
tion of  proportional,  208. 

Screen,  action  of  the  Bunsen,  62 ;  in- 
clined surface,  56;  wedge-shaped, 
57,  58;  paraffine  diffusing,  61;  the 
selenium,  102;  Thompson-Starling, 
60. 

Screen,  photo  metrical,  47;  reflecting, 
47;  diffusing,  48;  coloured,  60; 
classification  of,  51;  simple,  51; 
compound,  52 ;  materials  for  translu- 
cent, 49;  sensitiveness  of,  50;  incli- 
nation of,  51;  efficiency  of  various 
types,  99;  method  of  adjustment  of 
setting,  209;  illumination  change 
with  movement,  210. 

Secondary  sources  of  illumination  de- 
fined, 28. 

Sector  disk,  100,  239, 241 ;  principle  of, 
24. 

Selective  absorption  in  screens,  47. 

Selenium  screen,  102. 


268 


INDEX 


Sensations,  proposed  law  of  intensity, 
15 ;  law  of  the  differences,  17. 

Sensitiveness,  of  various  photometer 
screens,  99 ;  of  various  photometers, 
100;  of  the  screen,  50;  of  diffusing 
screens,  48;  of  photometer  settings, 
50;  of  the  flicker  photometer,  95; 
of  measurements  of  incandescent 
lamps,  191. 

Sight  field  of  Lummer-Brodhun  pho- 
tometer, the  composite,  74. 

Spectrophotometry,  87,  106,  232. 

Specular  reflection,  8,  47. 

Spherical  intensity,  mean,  38;  its 
value,  44 ;  practice  of,  41 ;  of  incan- 
descent lamps,  216 ;  by  spinning  the 
lamp,  217. 

Spinning  the  incandescent  lamp,  215. 

Standard  of  light,  photometrical,  re- 
quirements for,  112 ;  working  value, 
170. 

Standard  of  light,  the  ideal,  111 ;  basis 
for,  110;  rational,  107;  errors  in 
early  tests,  189. 

Standard  of  light,  the  so-called  "  ab- 
solute," 164;  acetylene,  195;  incan- 
descent filament,  187;  Netherlands 
Commission,  144;  petroleum  burn- 
ing, 193;  the  Siemen's,  167;  the 
Violle,  164,  166, 167. 

Standard  reading  for  incandescent 
lamp,  217. 

Storage  battery  for  lamp  tests,  202. 

Sugg  burner,  126. 

Surfaces,  reflecting  power,  table  of,  11. 

Suspensions  for  arc  lamp,  236. 


Table  of  ratios  for  photometer  bar,  258. 
Talbot's  law,  23,  25. 
Thompson  wedge,  92. 
Transparent  spot,  65. 

U 

Unit  intensity,  31. 

Unit  of  illuminating  power,  the  prac- 
tical, 34, 112. 
Unit  of  light,  30. 
Unit,  the  carcel,  124. 


Vector  distribution  from  light  source, 

28. 

Vereinskerze,  121. 
Violle  standard  of  light,  164. 
Vision,  effects  of  persistence,  18. 
Voltmeter,    sensitiveness   needed  for 

lamp  tests,  202. 

W 

Wave  length  and  colour,  7. 
Wave  train,  4. 
Weber  photometer,  78,  89,  106,  242, 

257;  constants  of,  84;  applications, 

82. 

Wedge-shaped  plates,  89. 
Wedge,  the  compensated,  90. 
Welsbach  gas  burner,  91,  246, 252. 
White  light,  normal,  13, 14  ;  from  arc, 

221. 

Whitman,  flicker  photometer,  92. 
Wiring  plan  for  photometer  table,  200 
Woodhouse  and  Rawson  lamp,  137. 


INDEX  TO   NAMES 


Abney,  110, 180, 187. 
Adams,  102. 
Anthony,  176. 
Audoin,  123, 125. 
Ayrton,  181,  186. 

B 

Bevard,  123, 125. 
Blondel,  110,  162,  221. 
Bonn,  64,  70. 
Bouguer,  52,  53,  56. 
Brodhun,  24,  70, 190. 

C 

Carcel,  123. 
Careau,  123. 
Center,  180, 181. 
Conroy,  59. 
Crova,  50. 

D 

Dibdin,  130, 136,  194. 
Doane,  234. 
Dove,  26. 
Draper,  103. 
Dumas,  123. 


E 


Elster,  61. 
Evans,  177,  178. 


F 

Faraday,  115. 
Ferguson,  180,  181. 
Ferry,  21,  25,  93. 
Forster,  167. 
Foster,  14,  18. 
Foucault,  50. 
Frankland,  113, 120. 
Freedman,  229. 


G 


Gerard,  231,  236. 
Gotz,  180. 


Harcourt,  132, 135, 137, 138, 141. 
Hartman,  194. 

Hefner- Alteneck,  65, 150, 193. 
Heim,  205. 
Heinrichs,  78. 
Helmholtz,  12,  13,  14, 15, 16, 17, 19,  26, 

50,  110,  111. 
Herschel,  56. 


Jamin,  33. 
Joly,  90. 


K 


Kepler,  52. 

Kirkham,  124. 

Klinck,  245. 

Kriiss,  65,  71, 106, 114, 118, 126, 167. 

Kurlbaum,  167. 


Ladd,  14, 16,  23,  24. 

Lambert,  33,  53,  67. 

Langley,  24. 

Laporte,  170. 

Lepinay,  85,  88. 

Leslie,  173. 

Lewes,  113. 

Liebenthal,  70,  141, 144,  152,  154,  155, 

157,  170, 198,  211,  216. 
Love,  120. 
Lummer,  24,  70, 167, 190. 

M 

Marks,  221,  229,  232. 
Matthews,  229,  235,  236. 
269 


270 


INDEX 


Maxwell,  13,  23,  108,  110,  111. 

Medley,  181, 186. 

Methven,  117,  119,   127,  128,  129,  130, 

140,  168. 
Miitzel,  108. 
Mylius,  167. 

N 

Nakano,  232. 
Nichols,  21,  22,  23,  195,  210,  232. 


Palaz,  226. 
Pedler,  103. 
Potter,  53. 
Preece,  96, 189. 
Preston,  6,  12. 
Puffer,  225. 
Purkinje,  26,  85. 


R 


Ram,  171,  173, 174,  178. 
Rawson,  130,  137. 
Regnault,  123. 
Ritchie,  55, 57,  61, 70. 
Rood,  7,  26,  93,  108. 
Riidorff,  63,  64,  70, 193. 
Rumford  (Thompson),  53. 

S 

Sabine,  89. 
Shepardson,  252,  253. 
Siemens,  167,  180, 193. 
Smith,  258. 


Spitta,  90. 

Stine,  34,  65, 163, 176,  221,  222. 

Stort,  245,  252. 

Strecker,  106. 

Sumpner,  10,  245. 

Swan,  70. 

Swinburne,  162. 


Thomas,  132, 186. 
Thompson,  B.,  53. 
Thompson,  S.  P.,  60, 162. 
Trotter,  96, 162,  226,  227,  228,  231, 
Tyndall,  49,  113. 


Violle,  49,  161,  162,  165,  166,  167,  168, 

194. 
Voit,  226. 

W 

Weber,  E.  H.,  15. 

Weber,  H.  S.,  172,  174, 176, 178,  180. 

Weber,  L.,  70,  78. 

Whitman,  92,  93. 

Williamson,  245. 

Willyoung,  206. 

Wright,  33,  255. 


Young,  12,  13,  110. 


Zollner,  165,  187. 


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